Postgraduate Course: Stochastic Modelling (MATH11029)

Course Outline
School	School of Mathematics	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 11 (Postgraduate)	Availability	Not available to visiting students
SCQF Credits	10	ECTS Credits	5
Summary	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.
Course description	Not entered

Entry Requirements (not applicable to Visiting Students)
Pre-requisites		Co-requisites
Prohibited Combinations	Students MUST NOT also be taking Stochastic Modelling (MATH10007)	Other requirements	None

Course Delivery Information
Not being delivered

Learning Outcomes
On completion of this course, the student will be able to: Formulate mathematically a range of real-life scenario of a stochastic process described in words. Demonstrate an understanding of discrete and continuous time stochastic processes by being able to calculate finite dimensional distributions. Analyse the transient behaviour of Markov chains, and classify their states. Demonstrate an understanding of stationary and limiting behaviour by deriving corresponding probability distributions, and first passage properties. Calculate the finite dimensional distributions of Poisson processes.