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Search the School of Mathematical Sciences
People matching "Stochastic modelling"
Courses matching "Stochastic modelling"
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Advanced Stochastic Modelling 
This course is part of the course offerings at Honours (Level IV) within Applied Mathematics.
Stochastic modelling plays an integral role in the analysis of many real-world systems. For example, in designing a telecommunications network it is important to be able to calculate performance measures such as mean utilisation of a resource, probability of packet loss, or expected time until a bu?er becomes empty. All of these are stochastic quantities that have to be derived via models that include randomness in their formulation. Similar examples can be given from most areas of science.
Assumed knowledge: Basic Probability (as obtained through, for example Mathematics for Information Technology I or Introduction to Mathematical Statistics II) Markov chains (as obtained through, for example, Applied Probability III).
More about this course...
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Financial Modelling III
Introduction to financial concepts and contingent claims, market
participants, and the use of various financial products.
One step binomial asset pricing models; non-arbitrage, the model
of Cox-Ross-Rubinstein, pricing European options, Call-Put parity,
forward contracts, contingent premium options, risk-neutral
probabilities, capital asset pricing model, exchange rates and interest-rate
parity formula, interest rate derivatives.
Multi-step binomial asset pricing models: the CRR model,
complimentary binomial distribution function, central limit theorem
and the Black-Scholes formula, calibration of CRR, volatility
estimation, American style option pricing, barrier options, exotics,
forwards and futures prices.
Implied Binomial Trees, Implied Volatility Trees, Applications to Real options.
More about this course...
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Financial Modelling Techniques III
This is a subject available to students enrolled
in the Bachelor of Finance degree. The aims and contents are
the same as for the subject Financial Modelling III. Introduction to financial concepts and contingent claims, market
participants, and the use of various financial products.
One step binomial asset pricing models; non-arbitrage, the model
of Cox-Ross-Rubinstein, pricing European options, Call-Put parity,
forward contracts, contingent premium options, risk-neutral
probabilities, capital asset pricing model, exchange rates and interest-rate
parity formula, interest rate derivatives.
Multi-step binomial asset pricing models: the CRR model,
complimentary binomial distribution function, central limit theorem
and the Black-Scholes formula, calibration of CRR, volatility
estimation, American style option pricing, barrier options, exotics,
forwards and futures prices.
Implied Binomial Trees, Implied Volatility Trees, Applications to Real options.
More about this course...
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Statistical Modelling III
One of the key requirements of an applied
statistician is the ability to formulate appropriate statistical
models and then apply them to data in order to answer the questions of
interest. Most often, such models can be seen as relating a
response variable to one or more explanatory variables.
For example, in a medical experiment we may seek to evaluate a new
treatment by relating patient outcome to treatment received while
allowing for background variables such as age, sex and disease
severity. In this course, various modelling strategies that extend
the basic linear model are developed. This includes non-linear
regression models, generalised linear models and regression models
with complex error structures. There is a strong practical emphasis
and the statistical packages
R and SAS are used at a more advanced level.
Who should take this course?
This course is core in the Statistics Major.
It is highly recommended for students who taken second-year
Statistics and wish to gain the edge in further study or research
by applying statistical modelling techniques in any area. Bivariate data
Measurement error and inherent variation
Regressions and correlation for a bivariate normal distribution
Regression of Y on x when values of x are chosen in advance
Intrinsically linear models
Both variables subject to error
Calibration lines (inverse regression)
The linear model
Conditional distributions from the multivariate normal distribution
The definition of the linear model
The linear model as an approximation
Estimation and properties of estimators
Definitions of residuals and regression diagnostics
Geometry of least squares
Transformations and generalised least squares
Non-linear regression
Regression models in experimental design
Factorial experiments - factors at 2 levels
Fractional factorials and inclusion of covariates by an example
Central composite designs
GLIM
Background to the generalised linear model (GLIM)
Distributions of the exponential type
Fitting a GLIM
Confidence intervals for parameters
Deviance
Binomial response -- logistic regression
Poisson response
Survival models
Life tables
Distributions for survival times
Proportional hazards model
More about this course...
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System Modelling and Simulation
System Modelling is the process of creating a model which imitates a system, generally in order to study some aspect of it's operation.
Many models are created to study real world systems, although models may be created for proposed systems. The main focus of this course will be on the use of simulation modelling for the modelling and investigation of such systems, although we will also look at some basic analytic mathematical models. Both techniques provide the modeller with a rich set of tools, which may be used to model many systems of interest. For example manufacturing systems, telecommunications networks, financial systems, games, ecosystems, ... Introduction to simulation firstly by performing hand simulation exercises in class and then by Introduction to a simulation package such as Opnet or Planimate. A small exercise using a simulation package is then performed by the students. A review of basic
probability theory, introduction to random number generation,
generation of random variates, analysis of simulation output and some basic analytic queueing models. Students complete a project in groups of two or three, writing a concise report of their investigations and findings. Students also give a final presentation of their findings to the class in the final week of semester.
More about this course...
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Telecommunications Systems Modelling III
Most real-world systems evolve under conditions of uncertainty and a knowledge of the state of the system at some time does not give us full information about the future behaviour of that system. In this course we show how to build stochastic models that translate information that we know, or are willing to assume, into information that we want to know. Although the main focus is on Telecommunications Systems that are relevant to today's society, such as the Internet, this subject places you in a position to be able to do much more. For example, systems that may be modelled with stochastic processes include : Engineering: Telecommunications, computer networks, industrial processes, dam construction. Biology: Evolution, Genetics, Epidemics, Species Interaction, Vegetation succession modelling.
Chemistry: Polymerisation, Bonding. Physics: Quantum Mechanics, Statistical Mechanics Economics and Finance: Portfolio management, interactions of complex systems. Management Science: That is, Call Centres, Networks of Queues. Continuous-time Markov chains, analysis of transient behaviour, the stationary distribution, hitting probabilities and expected hitting times.
Traffic models.
Birth and death processes.
Basic teletraffic formulae, evaluation of delay, congestion and bu?er size performance measures for simple queues and single network links.
Evaluation of exact and approximate performance measures for networks.
The concept of e?ective bandwidth and its use in the calculation of quality of service criteria.
Modelling of various forms of TCP/IP and calculation of some performance measures for networks operating under these protocols.
More about this course...
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Events matching "Stochastic modelling"
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Mathematical modelling of multidimensional tissue growth 16:10 Tue 24 Oct 06 | Benham Lecture Theatre | Professor John King
Abstract...Some simple continuum-mechanics-based models for the
growth of biological tissue will be formulated and their properties
(particularly with regard to stability) described.
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Modelling gene networks: the case of the quorum sensing network in bacteria. 15:10 Fri 1 Jun 07 | G08, Mathematics Building, University of Adelaide | Dr Adrian Koerber
Abstract...The quorum sensing regulatory gene-network is employed by bacteria to provide a measure of their population-density and switch their behaviour accordingly. I will present an overview of quorum sensing in bacteria together with some of the modelling approaches I\'ve taken to describe this system. I will also discuss how this system relates to virulence and medical treatment, and the insights gained from the mathematics.
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Global and Local stationary modelling in finance: Theory and empirical evidence 14:10 Thu 10 Apr 08 | G04, Napier Building, University of Adelaide | Prof. Dominique Guégan | Universite Paris 1 Pantheon-Sorbonne
Abstract...To model real data sets using second order stochastic processes imposes that the data sets verify the second order stationarity condition. This stationarity condition concerns the unconditional moments of the process. It is in that context that most of models developed from the sixties' have been studied; We refer to the ARMA processes (Brockwell and Davis, 1988), the ARCH, GARCH and EGARCH models (Engle, 1982, Bollerslev, 1986, Nelson, 1990), the SETAR process (Lim and Tong, 1980 and Tong, 1990), the bilinear model (Granger and Andersen, 1978, Guégan, 1994), the EXPAR model (Haggan and Ozaki, 1980), the long memory process (Granger and Joyeux, 1980, Hosking, 1981, Gray, Zang and Woodward, 1989, Beran, 1994, Giraitis and Leipus, 1995, Guégan, 2000), the switching process (Hamilton, 1988). For all these models, we get an invertible causal solution under specific conditions on the parameters, then the forecast points and the forecast intervals are available.
Thus, the stationarity assumption is the basis for a general asymptotic theory for identification, estimation and forecasting. It guarantees that the increase of the sample size leads to more and more information of the same kind which is basic for an asymptotic theory to make sense.
Now non-stationarity modelling has also a long tradition in econometrics. This one is based on the conditional moments of the data generating process. It appears mainly in the heteroscedastic and volatility models, like the GARCH and related models, and stochastic volatility processes (Ghysels, Harvey and Renault 1997). This non-stationarity appears also in a different way with structural changes models like the switching models (Hamilton, 1988), the stopbreak model (Diebold and Inoue, 2001, Breidt and Hsu, 2002, Granger and Hyung, 2004) and the SETAR models, for instance. It can also be observed from linear models with time varying coefficients (Nicholls and Quinn, 1982, Tsay, 1987).
Thus, using stationary unconditional moments suggest a global stationarity for the model, but using non-stationary unconditional moments or non-stationary conditional moments or assuming existence of states suggest that this global stationarity fails and that we only observe a local stationary behavior.
The growing evidence of instability in the stochastic behavior of stocks, of exchange rates, of some economic data sets like growth rates for instance, characterized by existence of volatility or existence of jumps in the variance or on the levels of the prices imposes to discuss the assumption of global stationarity and its consequence in modelling, particularly in forecasting. Thus we can address several questions with respect to these remarks.
1. What kinds of non-stationarity affect the major financial and economic data sets? How to detect them?
2. Local and global stationarities: How are they defined?
3. What is the impact of evidence of non-stationarity on the statistics computed from the global non stationary data sets?
4. How can we analyze data sets in the non-stationary global framework? Does the asymptotic theory work in non-stationary framework?
5. What kind of models create local stationarity instead of global stationarity? How can we use them to develop a modelling and a forecasting strategy?
These questions began to be discussed in some papers in the economic literature. For some of these questions, the answers are known, for others, very few works exist. In this talk I will discuss all these problems and will propose 2 new stategies and modelling to solve them. Several interesting topics in empirical finance awaiting future research will also be discussed.
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Betti's Reciprocal Theorem for Inclusion and Contact Problems 15:10 Fri 1 Aug 08 | G03, Napier Building, University of Adelaide | Prof. Patrick Selvadurai | Department of Civil Engineering and Applied Mechanics, McGill University
Abstract...Enrico Betti (1823-1892) is recognized in the mathematics community for his pioneering contributions to topology. An equally important contribution is his formulation of the reciprocity theorem applicable to elastic bodies that satisfy the classical equations of linear elasticity. Although James Clerk Maxwell (1831-1879) proposed a law of reciprocal displacements and rotations in 1864, the contribution of Betti is acknowledged for its underlying formal mathematical basis and generality. The purpose of this lecture is to illustrate how Betti's reciprocal theorem can be used to full advantage to develop compact analytical results for certain contact and inclusion problems in the classical theory of elasticity. Inclusion problems are encountered in number of areas in applied mechanics ranging from composite materials to geomechanics. In composite materials, the inclusion represents an inhomogeneity that is introduced to increase either the strength or the deformability characteristics of resulting material. In geomechanics, the inclusion represents a constructed material region, such as a ground anchor, that is introduced to provide load transfer from structural systems. Similarly, contact problems have applications to the modelling of the behaviour of indentors used in materials testing to the study of foundations used to distribute loads transmitted from structures. In the study of conventional problems the inclusions and the contact regions are directly loaded and this makes their analysis quite straightforward. When the interaction is induced by loads that are placed exterior to the indentor or inclusion, the direct analysis of the problem becomes inordinately complicated both in terns of formulation of the integral equations and their numerical solution. It is shown by a set of selected examples that the application of Betti's reciprocal theorem leads to the development of exact closed form solutions to what would otherwise be approximate solutions achievable only through the numerical solution of a set of coupled integral equations.
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Probabilistic models of human cognition 15:10 Fri 29 Aug 08 | G03, Napier Building, University of Adelaide | Dr Daniel Navarro | School of Psychology, University of Adelaide
Abstract...Over the last 15 years a fairly substantial psychological literature has developed in which human reasoning and decision-making is viewed as the solution to a variety of statistical problems posed by the environments in which we operate. In this talk, I briefly outline the general approach to cognitive modelling that is adopted in this literature, which relies heavily on Bayesian statistics, and introduce a little of the current research in this field. In particular, I will discuss work by myself and others on the statistical basis of how people make simple inductive leaps and generalisations, and the links between these generalisations and how people acquire word meanings and learn new concepts. If time permits, the extensions of the work in which complex concepts may be characterised with the aid of nonparametric Bayesian tools such as Dirichlet processes will be briefly mentioned.
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Mathematical modelling of blood flow in curved arteries 15:10 Fri 12 Sep 08 | G03, Napier Building, University of Adelaide | Dr Jennifer Siggers | Imperial College London
Abstract...Atherosclerosis, characterised by plaques, is the most common arterial
disease. Plaques tend to develop in regions of low mean wall shear
stress, and regions where the wall shear stress changes direction during
the course of the cardiac cycle. To investigate the effect of the
arterial geometry and driving pressure gradient on the wall shear stress
distribution we consider an idealised model of a curved artery with
uniform curvature. We assume that the flow is fully-developed and seek
solutions of the governing equations, finding the effect of the
parameters on the flow and wall shear stress distribution. Most
previous work assumes the curvature ratio is asymptotically small;
however, many arteries have significant curvature (e.g. the aortic arch
has curvature ratio approx 0.25), and in this work we consider in
particular the effect of finite curvature.
We present an extensive analysis of curved-pipe flow driven by a steady
and unsteady pressure gradients. Increasing the curvature causes the
shear stress on the inside of the bend to rise, indicating that the risk
of plaque development would be overestimated by considering only the
weak curvature limit.
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Assisted reproduction technology: how maths can contribute 13:10 Wed 22 Oct 08 | Napier 210 | Dr Yvonne Stokes
Abstract...Most people will have heard of IVF (in vitro fertilisation), a
technology for helping infertile couples have a baby. Although there are
many IVF babies, many will also know that the success rate is still low
for the cost and inconvenience involved. The fact that some women
cannot make use of IVF because of life-threatening consequences is less
well known but motivates research into other technologies, including
IVM (in vitro maturation).
What has all this to do with maths? Come along and find out how
mathematical modelling is contributing to understanding and
improvement in this important and interesting field.
Media for this event...
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Oceanographic Research at the South Australian Research and Development Institute: opportunities for collaborative research 15:10 Fri 21 Nov 08 | Napier G04 | Associate Prof John Middleton | South Australian Research and Development Institute
Abstract...
Increasing threats to S.A.'s fisheries and marine environment have underlined the increasing need for soundly based research into the ocean circulation and ecosystems (phyto/zooplankton) of the shelf and gulfs. With support of Marine Innovation SA, the Oceanography Program has within 2 years, grown to include 6 FTEs and a budget of over $4.8M. The program currently leads two major research projects, both of which involve numerical and applied mathematical modelling of oceanic flow and ecosystems as well as statistical techniques for the analysis of data. The first is the implementation of the Southern Australian Integrated Marine Observing System (SAIMOS) that is providing data to understand the dynamics of shelf boundary currents, monitor for climate change and understand the phyto/zooplankton ecosystems that under-pin SA's wild fisheries and aquaculture. SAIMOS involves the use of ship-based sampling, the deployment of underwater marine moorings, underwater gliders, HF Ocean RADAR, acoustic tracking of tagged fish and Autonomous Underwater vehicles.
The second major project involves measuring and modelling the ocean circulation and biological systems within Spencer Gulf and the impact on prawn larval dispersal and on the sustainability of existing and proposed aquaculture sites. The discussion will focus on opportunities for collaborative research with both faculty and students in this exciting growth area of S.A. science.
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Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations 15:10 Fri 19 Jun 09 | LG29 | Prof. Eckhard Platen | University of Technology, Sydney
Abstract...This paper introduces a new class of numerical
schemes for the pathwise approximation of solutions of stochastic
differential equations (SDEs). The proposed family of strong
predictor-corrector Euler methods are designed to handle scenario
simulation of solutions of SDEs. It has the potential to overcome
some of the numerical instabilities that are often experienced
when using the explicit Euler method. This is of importance, for
instance, in finance where martingale dynamics arise for solutions
of SDEs with multiplicative diffusion coefficients. Numerical
experiments demonstrate the improved asymptotic stability
properties of the proposed symmetric predictor-corrector Euler
methods.
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News matching "Stochastic modelling"
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Success in Learning and Teaching Grants The School of Mathematical Sciences has been awarded two Faculty L&T awards. Congratulations to Dr David Green for his successful grant "One Simulation Modelling Instruction Module" and to Drs Adrian Koerber, Paul McCann and Jim Denier for their successful grant "Graphics Calculators and beyond". Posted Tue 11 Mar 08.
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Australian Research Council Discovery Project Successes Congratulations to the following members of the School for their
success in the ARC Discovery Grants which were announced recently.
- A/Prof M Roughan; Prof H Shen $315K Network Management in a World of Secrets
- Prof AJ Roberts; Dr D Strunin $315K
Effective and accurate model dynamics, deterministic and stochastic,
across multiple space and time scales
- A/Prof J Denier; Prof AP Bassom $180K A novel approach to controlling boundary-layer separation
Posted Wed 17 Sep 08.
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Sam Cohen wins prize for best student talk at ANZIAM 2009 Congratulations to Mr Sam Cohen, a PhD student within the School, who was awarded the T. M. Cherry Prize for the best student paper at the 2009 meeting of ANZIAM for his talk on
A general theory of backward stochastic difference equations. Posted Fri 6 Feb 09.
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Publications matching "Stochastic modelling"
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Generalized solutions to abstract stochastic problems
Melnikova, I; Filinkov, Alexei, Integral Transforms and Special Functions 20 (199–206) 2009 |
Hitting probabilities and hitting times for stochastic fluid flows the bounded model
Bean, Nigel; O'Reilly, Malgorzata; Taylor, P, Probability in the Engineering and Informational Sciences 23 (121–147) 2009 |
On the beneficial impact of strong correlations for anomaly detection
Roughan, Matthew, Stochastic Models (1–27) 2009 |
Stochastic Resonance From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, (Cambridge University Press) 2008 |
A markovian regime-switching stochastic differential game for portfolio risk minimization
Elliott, Robert; Siu, T, 2008 American Control Conference, Washington 11/06/08 |
Modelling Water Blending-Sensitivity of Optimal Policies
Webby, Roger; Green, David; Metcalfe, Andrew, 17th Biennial Congress on Modeling and Simulation, New Zealand 01/12/08 |
Stochastic cyclone modelling in the Bay of Bengal
Need, Steven; Lambert, Martin; Metcalfe, Andrew; Sen, D, Water Down Under 2008, Adelaide 14/04/08 |
A non-linear filter
Elliott, Robert; Leung, H; Deng, J, Stochastic Analysis and Applications 26 (856–862) 2008 |
Algorithms for the Laplace-Stieltjes transforms of first return times for stochastic fluid flows
Bean, Nigel; O'Reilly, Malgorzata; Taylor, Peter, Methodology and Computing in Applied Probability 10 (381–408) 2008 |
Characterization of matrix-exponential distributions
Bean, Nigel; Fackrell, Mark; Taylor, Peter, Stochastic Models 24 (339–363) 2008 |
Evolving gene frequencies in a population with three possible alleles at a locus
Hajek, Bronwyn; Broadbridge, P; Williams, G, Mathematical and Computer Modelling 47 (210–217) 2008 |
Modelling survival in acute severe illness: Cox versus accelerated failure time models
Moran, John; Bersten, A; Solomon, Patricia; Edibam, C; Hunt, T, Journal of Evaluation in Clinical Practice 14 (83–93) 2008 |
Stochastic dynamic programming (SDP) with a conditional value-at-risk (CVaR) criterion for management of storm-water
Piantadosi, J; Metcalfe, Andrew; Howlett, P, Journal of Hydrology 348 (320–329) 2008 |
Stochastic linear programming and conditional value-at-risk for water resources management
Webby, Roger; Boland, J; Howlett, P; Metcalfe, Andrew, The ANZIAM Journal - On-line full-text 48 (885–898) 2008 |
The mathematical modelling of rotating capillary tubes for holey-fibre manufacture
Voyce, Christopher; Fitt, A; Monro, Tanya, Journal of Engineering Mathematics 60 (69–87) 2008 |
Normal form transforms separate slow and fast modes in stochastic dynamical systems
Roberts, Anthony John, Physics Letters A 387 (12–38) 2008 |
Computer algebra derives discretisations via self-adjoint multiscale modelling (Unpublished)
Roberts, Anthony John, |
Model subgrid microscale interactions to accurately discretise stochastic partial differential equations.
Roberts, Anthony John, |
Inverse groundwater modelling in the Willunga Basin, South Australia
Knowles, I; Teubner, Michael; Yan, A; Rasser, Paul; Lee, Jong, Hydrogeology Journal 15 (1107–1118) 2007 |
The Mekong-applications of value at risk (VAR) and conditional value at risk (CVAR) simulation to the benefits, costs and consequences of water resources development in a large river basin
Webby, Roger; Adamson, Peter; Boland, J; Howlett, P; Metcalfe, Andrew; Piantadosi, J, Ecological Modelling 201 (89–96) 2007 |
The solution of a free boundary problem related to environmental management systems
Elliott, Robert; Filinkov, Alexei, Stochastic Analysis and Applications 25 (1189–1202) 2007 |
Computer algebra derives normal forms of stochastic differential equations
Roberts, Anthony John, |
Drought forecasting using adaptive stochastic models in New South Wales
Wong, Hui; Osti, Alexander; Lambert, Martin; Metcalfe, Andrew, 30th Hydrology and Water Resources Symposium, Launceston, Tasmania 04/12/06 |
Modelling extreme rainfall and tidal anomaly
Need, Steven; Lambert, Martin; Metcalfe, Andrew, 30th Hydrology and Water Resources Symposium, Launceston, Tasmania 04/12/06 |
Modelling multivariate extreme flood events
Wong, Hui; Need, Steven; Adamson, Peter; Lambert, Martin; Metcalfe, Andrew, 30th Hydrology and Water Resources Symposium, Launceston, Tasmania 04/12/06 |
Data-recursive smoother formulae for partially observed discrete-time Markov chains
Elliott, Robert; Malcolm, William, Stochastic Analysis and Applications 24 (579–597) 2006 |
Mathematical modelling of oxygen concentration in bovine and murine cumulus-oocyte complexes
Clark, Alys; Stokes, Yvonne; Lane, Michelle; Thompson, Jeremy, Reproduction 131 (999–1006) 2006 |
Optimal information transmission in nonlinear arrays through suprathreshold stochastic resonance
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, Physics Letters A 352 (183–189) 2006 |
Stochastic volatility model with filtering
Elliott, Robert; MIao, H, Stochastic Analysis and Applications 24 (661–683) 2006 |
Resolving the multitude of microscale interactions accurately models stochastic partial differential equations
Roberts, Anthony John, London Mathematical Society. Journal of Computation and Mathematics 9 (193–221) 2006 |
Stochastic elastohydrodynamics of a microcantilever oscillating near a wall - art. no. 050801
Clarke, Richard; Jensen, O; Billingham, J; Pearson, A; Williams, P, Physical Review Letters 9605 (801-01–801-04) 2006 |
An algorithmic estimation scheme for hybrid stochastic systems
Malcolm, William; Elliott, Robert; Dufour, F; Arulampalam, M, The 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, Seville, Spain 12/12/05 |
Analog to digital conversion using suprathreshold stochastic resonance
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, The SPIE International Symposium on Smart Structures, Devices, and Systems II, Sydney, Australia 13/12/04 |
Exact smoothers for discrete-time hybrid stochastic systems
Elliott, Robert; Malcolm, William; Dufour, F, The 44th IEEE Conference on Decision and Control and the European Control Conference, Seville, Spain 12/12/05 |
Algorithms for return probabilities for stochastic fluid flows
Bean, Nigel; O'Reilly, Malgorzata; Taylor, Peter, Stochastic Models 21 (149–184) 2005 |
An analytic modelling approach for network routing algorithms that use "ant-like" mobile agents
Bean, Nigel; Costa, Andre, Computer Networks-The International Journal of Computer and Telecommunications Networking 49 (243–268) 2005 |
An inverse modelling technique for glass forming by gravity sagging
Agnon, Y; Stokes, Yvonne, European Journal of Mechanics B-Fluids 24 (275–287) 2005 |
Hidden Markov chain filtering for a jump diffusion model
Wu, P; Elliott, Robert, Stochastic Analysis and Applications 23 (153–163) 2005 |
Hidden Markov filter estimation of the occurrence time of an event in a financial market
Elliott, Robert; Tsoi, A, Stochastic Analysis and Applications 23 (1165–1177) 2005 |
Hitting probabilities and hitting times for stochastic fluid flows
Bean, Nigel; O'Reilly, Malgorzata; Taylor, Peter, Stochastic Processes and their Applications 115 (1530–1556) 2005 |
Reliability of supply between production lines
Green, David; Metcalfe, Andrew, Stochastic Models 21 (449–464) 2005 |
Optimal quantization and suprathreshold stochastic resonance
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, Fluctuations and noise in biological, biophysical, and biomedical systems III, Austin, Texas, USA 24/05/05 |
Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: "quorum" sensing by a single bacterium
Koerber, Adrian; King, J; Williams, P, Journal of Mathematical Biology 50 (440–488) 2005 |
Filtering, smoothing and M-ary detection with discrete time poisson observations
Elliott, Robert; Malcolm, William; Aggoun, L, Stochastic Analysis and Applications 23 (939–952) 2005 |
Finite-dimensional filtering and control for continuous-time nonlinear systems
Elliott, Robert; Aggoun, L; Benmerzouga, A, Stochastic Analysis and Applications 22 (499–505) 2005 |
Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations
Roberts, Anthony John, |
Investigation and modelling of traffic issues in immersive audio environments
McMahon, Jeremy; Rumsewicz, Michael; Boustead, P; Safaei, F, 2004 IEEE International Conference on Communications, Paris, France 20/06/04 |
A deterministic discretisation-step upper bound for state estimation via Clark transformations
Malcolm, William; Elliott, Robert; Van Der Hoek, John, J.A.M.S.A. Journal of Applied Mathematics and Stochastic Analysis 2004 (371–384) 2004 |
Modelling thirty-day mortality in the acute respiratory distress syndrome (ARDS) in an adult ICU
Moran, John; Solomon, Patricia; Fox, V; Salagaras, M; Williams, P; Quinlan, K; Bersten, A, Anaesthesia and Intensive Care 32 (317–329) 2004 |
Development of Non-Homogeneous and Hierarchical Hidden Markov Models for Modelling Monthly Rainfall and Streamflow Time Series
Whiting, Julian; Lambert, Martin; Metcalfe, Andrew; Kuczera, George, World Water and Environmental Resources Congress (2004), Salt Lake City, Utah, USA 27/06/04 |
Conditional moment generating functions for integrals and stochastic integrals
Charalambous, C; Elliott, Robert; Krishnamurthy, V, Siam Journal on Control and Optimization 42 (1578–1603) 2004 |
Stochastic modelling of tidal anomaly for estimation of flood risk in coastal areas
Ahmer, Ingrid; Lambert, Martin; Leonard, Michael; Metcalfe, Andrew, 28th International Hydrology and Water Resources Symposium, Wollongong, NSW, Australia 10/11/03 |
The data processing inequality and stochastic resonance
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, Noise in Complex Systems and Stochastic Dynamics, Santa Fe, New Mexico, USA 01/06/03 |
A Probabilistic algorithm for determining the fundamental matrix of a block M/G/1 Markov chain
Hunt, Emma, Mathematical and Computer Modelling 38 (1203–1209) 2003 |
A philosophy for the modelling of realistic nonlinear systems
Howlett, P; Torokhti, Anatoli; Pearce, Charles, Proceedings of the American Mathematical Society 132 (353–363) 2003 |
An approximate formula for the stress intensity factor for the pressurized star crack
Clements, David; Widana, Inyoman, Mathematical and Computer Modelling 37 (689–694) 2003 |
Effect of environmental fluctuations on the dynamic composition of engineered cartilage: a deterministic model in stochastic environment
Saha, Asit; Mazumdar, Jagan; Morsi, Y, IEEE Transactions on NanoBioscience 2 (158–162) 2003 |
Method of hybrid approximations for modelling of multidimensional nonlinear systems
Torokhti, Anatoli; Howlett, P; Pearce, Charles, Multidimensional Systems and Signal Processing 14 (397–410) 2003 |
Modelling persistence in annual Australian point rainfall
Whiting, Julian; Lambert, Martin; Metcalfe, Andrew, Hydrology and Earth System Sciences 7 (197–211) 2003 |
On the Clark-Ocone theorem for fractional Brownian motions with Hurst parameter bigger than a half
Bender, C; Elliott, Robert, Stochastics and Stochastic Reports 75 (391–405) 2003 |
Optimal mathematical models for nonlinear dynamical systems
Torokhti, Anatoli; Howlett, P; Pearce, Charles, Mathematical and Computer Modelling of Dynamical Systems 9 (327–343) 2003 |
Rumours, epidemics, and processes of mass action: Synthesis and analysis
Dickinson, Rowland; Pearce, Charles, Mathematical and Computer Modelling 38 (1157–1167) 2003 |
Stochastic resonance and data processing inequality
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, Electronics Letters 39 (1287–1288) 2003 |
Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics
Roberts, Anthony John, chapter in Nonlinear dynamics: from lasers to butterflies (World Scientific Publishing) 257–313, 2003 |
Stochastic Differential Equations in Hilbert Spaces
Filinkov, Alexei; Maizurna, Isna; Sorenson, J; Van Der Hoek, John, chapter in Applicable Mathematics in the Golden Age (Morgan & Claypool) 32–169, 2003 |
A step towards holistic discretisation of stochastic partial differential equations
Roberts, Anthony John, The ANZIAM Journal 45 (C1–C15) 2003 |
Modelling host tissue degradation by extracellular bacterial pathogens
King, J; Koerber, Adrian; Croft, J; Ward, J; Williams, P; Sockett, R, Mathematical Medicine and Biology (Print Edition) 20 (227–260) 2003 |
Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity
Melnik, R; Roberts, Anthony John, Zeitschrift fur Angewandte Mathematik und Mechanik 83 (93–104) 2003 |
Modelling the dynamics of turbulent floods
Mei, Z; Roberts, Anthony John; Li, Z, Siam Journal on Applied Mathematics 63 (423–458) 2003 |
Coastal flood modelling: Allowing for dependence between rainfall and tidal anomaly
Ahmer, Ingrid; Metcalfe, Andrew; Lambert, Martin; Deans, J, EMAC 2002, Brisbane, Australia 29/09/02 |
A characterization of suprathreshold stochastic resonance in an array of comparators by correlation coefficient
McDonnell, Mark; Abbott, Derek; Pearce, Charles, Fluctuation and Noise Letters 2 (L205–L220) 2002 |
A mathematical study of peristaltic transport of a Casson fluid
Mernone, Anacleto; Mazumdar, Jagan; Lucas, S, Mathematical and Computer Modelling 35 (895–912) 2002 |
Bivariate stochastic modelling of ephemeral streamflow
Cigizoglu, H; Adamson, Peter; Metcalfe, Andrew, Hydrological Processes 16 (1451–1465) 2002 |
Differential equations in spaces of abstract stochastic distributions
Filinkov, Alexei; Sorensen, Julian, Stochastics and Stochastic Reports 72 (129–173) 2002 |
Truncation and augmentation of level-independent QBD processes
Latouche, Guy; Taylor, Peter, Stochastic Processes and their Applications 99 (53–80) 2002 |
Stochastic models and simulation
Metcalfe, Andrew, chapter in Research methods for postgraduates (Oxford University Press) 292–299, 2002 |
Robust continuous-time smoothers without two-sided stochastic integrals
Krishnamurthy, V; Elliott, Robert, IEEE Transactions on Automatic Control 47 (1824–1841) 2002 |
Fractional Brownian motion and financial modelling
Elliott, Robert; Van Der Hoek, John, chapter in Mathematical Finance (Birkhauser) 140–151, 2001 |
Integrated solutions of stochastic evolution equations with additive noise
Filinkov, Alexei; Maizurna, Isna, Bulletin of the Australian Mathematical Society 64 (281–290) 2001 |
Statistical modelling and prediction associated with the HIV/AIDS epidemic
Solomon, Patricia; Wilson, Susan, The Mathematical Scientist 26 (87–102) 2001 |
Stochastic flows and the forward measure
Elliott, Robert; Van Der Hoek, John, Finance and Stochastics 5 (511–525) 2001 |
The Mx/G/1 queue with queue length dependent service times
Choi, B; Kim, Y; Shin, Y; Pearce, Charles, J.A.M.S.A. Journal of Applied Mathematics and Stochastic Analysis 14 (399–419) 2001 |
The modelling and numerical simulation of causal non-linear systems
Howlett, P; Torokhti, Anatoli; Pearce, Charles, Nonlinear Analysis-Theory Methods & Applications 47 (5559–5572) 2001 |
Modelling Overflow Traffic from Terrestrial Networks into Satellite Networks
Green, David, 8th International Conference on Telecommunications (June 2001), Bucharest, Romania 04/06/01 |
Modelling Service Time Distribution in Cellular Networks Using Phase-Type Service Distributions
Green, David; Asenstorfer, J; Jayasuriya, A, |
A continuous time kronecker's lemma and martingale convergence
Elliott, Robert, Stochastic Analysis and Applications 19 (433–437) 2001 |
Mathematical modelling of quorum sensing in bacteria
Ward, J; King, J; Koerber, Adrian; Williams, P; Croft, J; Sockett, R, Mathematical Medicine and Biology (Print Edition) 18 (263–292) 2001 |
A brief survey and synthesis of the roles of time in petri nets
Bowden, Fred David John, Mathematical and Computer Modelling 31 (55–68) 2000 |
A new perspective on the normalization of invariant measures for loss networks and other product form systems
Bean, Nigel; Stewart, Mark, Mathematical and Computer Modelling 31 (47–54) 2000 |
Algorithms for second moments in batch-movement queueing systems
Hunt, Emma, Mathematical and Computer Modelling 31 (299–305) 2000 |
Biomathematical modelling of physiological fluids using a Casson fluid with emphasis to peristalsis
Mernone, Anacleto; Mazumdar, Jagan, Australasian Physical and Engineering Sciences in Medicine 23 (94–100) 2000 |
Disease surveillance and data collection issues in epidemic modelling
Solomon, Patricia; Isham, V, Statistical Methods in Medical Research 9 (259–277) 2000 |
Maximal profit dimensioning and tariffing of loss networks with cross-connects
Bean, Nigel; Brown, Deborah; Taylor, Peter, Mathematical and Computer Modelling 31 (21–30) 2000 |
Quasi-reversibility and networks of queues with nonstandard batch movements
Taylor, Peter, Mathematical and Computer Modelling 31 (335–341) 2000 |
Quasistationary distributions for level-dependent quasi-birth-and-death processes
Bean, Nigel; Pollett, P; Taylor, Peter, Stochastic Models 16 (511–541) 2000 |
The exact solution of the general stochastic rumour
Pearce, Charles, Mathematical and Computer Modelling 31 (289–298) 2000 |
Weak and generalized solutions to abstract stochastic equations
Melnikova, I; Filinkov, Alexei, Doklady Mathematics 62 (373–377) 2000 |
When is a MAP poisson?
Bean, Nigel; Green, David, Mathematical and Computer Modelling 31 (31–46) 2000 |
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