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		Other requirements	None

Course Delivery Information

Academic year 2015/16, 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 %
Additional Information (Assessment)	See 'Breakdown of Assessment Methods' and 'Additional Notes' above.
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S2 (April/May)	MSc Stochastic Modelling		2:00

Learning Outcomes
1. Basic understanding of stochastic processes and their characterization 2. Basic probabilistic reasoning skills 3. Ability to model dynamic systems with noise, applications include reliability theory, inventory theory, queueing theory, telecommunication networks, biological systems 4. Ability to classify states of a Markov chain 5. Understanding transient and stationary behaviour of Markov chains and deriving stationary distributions 6. Ability to model and analyze arrival processes as Poisson processes