Applied Probability III
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Description
Many processes in the real world involve some random variation superimposed on a deterministic structure. For example, the experiment of flipping a coin is best studied by treating the outcome as a random one. Mathematical probability has its origins in games of chance with dice and cards, originating in the fifteenth and sixteenth centuries. This course aims to provide a basic toolkit for modelling and analyzing discretetime problems in which there is a significant probabilistic component. We will consider Markov chain examples in the course including population branching processes (with application to genetics), random walks (with application to games), and more general discrete time examples using Martingales.
Objective
to introduce students to the basic tools used by applied probabilists, and
to give students a thorough grounding in the theory of discretetime
Markov chains on a countable state space. To provide a thorough grounding in discretetime Markov chains on a countable state space. The student will obtain an indepth knowledge of Markov chains both from a theoretical and a modelling viewpoint.
Content
Topics covered are: basic probability and measure theory, discrete time Markov chains, hitting probabilities and hitting time theorems, population branching processes, inhomogeneous random walks on the line, solidarity properties and communicating classes, necessary and sufficient conditions for transience and positive recurrence, global balance, partial balance, reversibility, Martingales, stopping times and stopping theorems with a link to Brownian motion.


Year 
Semester 
Level 
Units 
2013 
1 
3 
3 
Graduate attributes
Linkage future
The material covered in this unit is useful for
APP MTH 3016 Telecommunications Systems Modelling III.
Recommended text
References: a list will be provided in lectures
