Applied Probability III

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Description

Many processes in the real world involve some random variation superimposed on a deterministic structure. Often -- as in games -- the random component is the dominant part. This course aims to provide a basic toolkit for modelling and analyzing discrete-time problems in which there is a significant probabilistic component. Markov chain examples in the course include population branching processes (with application to genetics), random walks (with application to tennis and other games), and processes with an over--riding cost structure.

Objective

to introduce students to the basic tools used by applied probabilists, and to give students a thorough grounding in the theory of discrete-time Markov chains on a countable state space. To provide a thorough grounding in discrete-time Markov chains on a countable state space. The student will obtain an in-depth knowledge of Markov chains both from a theoretical and a modelling viewpoint.

Content

Topics covered are: hitting probabilities and hitting time theorems, (including extremal versions), population branching processes, inhomogeneous random walks on the line, transient, recurrent and ephemeral states, communicating classes, solidarity properties, necessary and sufficient conditions for transience and positive recurrence, global balance, partial balance, reversibility, rewards on Markov chains, and the policy improvement algorithm.

David Green Lecturer for this course

Delivery

36 hours of lectures and tutorials.

Assessment

Ongoing assessment 30%, exam 70%.

Graduate attributes

• Applying mathematical knowledge (1)
• Interpreting data and drawing conclusions (2)
• Formulating mathematical problems (3)
• Problem solving skills (4)
• Flexibility in working environment (5)
• Team participation and leadership (7)

Linkage past

Prerequisite is MATHS 1007A/B Mathematics I or MATHS 2004 Mathematics IIM. It will help to have done the probability part of APP MTH 2008 Operations Research II and either the probability part of MATHS 1008 Mathematics for Information Technology or STATS 2002 Introduction to Mathematical Statistics II.

Linkage present

A sister unit is APP MTH 3016 Telecommunications Systems Modelling III. Other units relating to Operations Research are APP MTH 3014 Optimisation III, APP MTH 3005 Mathematical Programming !III and APP MTH 3010 Variational Methods and Optimal Control III.

Linkage future

The material covered in this unit is useful for APP MTH 3016 Telecommunications Systems Modelling III.

Restrictions

None.

Recommended text

References: a list will be provided in lectures