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Semester 1

Stochastic Modelling (MATH10007)

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Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.

Course Summary

This is an advanced probability course dealing with discrete and continuous time Markov chains. The course covers the fundamental theory, and provides many examples. Markov chains has countless applications in many fields raging from finance, operation research and optimization to biology, chemistry and physics.

Course Description

Markov Chains in discrete time: classification of states, first passage and recurrence times, absorption problems, stationary and limiting distributions.Markov Processes in continuous time: Poisson processes, birth-death processes.The Q matrix, forward and backward differential equations, imbedded Markov Chain, stationary distribution. Syllabus summary: Probability review: Conditional probability, basic definition of stochastic processes. Discrete-time Markov chains: Modelling of real life systems as Markov chains, transient behaviour, limiting behaviour and classification of states, first passage and recurrence times, absorption problems, ergodic theorems, Markov chains with costs and rewards, reversibility. Poisson processes: Exponential distribution, counting processes, alternative definitions of Poisson processes, splitting, superposition and uniform order statistics properties, non-homogeneous Poisson processes. Continuous-time Markov chains: transient behaviour, limiting behaviour and classification of states in continuous time, ergodicity, basic queueing models.

Assessment Information

Written Exam 95%, Coursework 5%, Practical Exam 0%

Additional Assessment Information

Coursework 5%, Examination 95%

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