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

Academic year 2019/20, Not available to visiting students (SS1)		Quota: None
Course Start	Semester 2
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 20, Seminar/Tutorial Hours 10, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 66 )
Assessment (Further Info)	Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S2 (April/May)	MSc Stochastic Modelling		2:00

Learning Outcomes
On completion of this course, the student will be able to: Demonstrate basic understanding of stochastic processes and their characterization, as well as basic probabilistic reasoning skills. Model dynamic systems with noise, applications include reliability theory, inventory theory, queueing theory, telecommunication networks, biological systems. Classify states of a Markov chain. Understand transient and stationary behaviour of Markov chains and deriving stationary distributions. Model and analyze arrival processes as Poisson processes.