Stochastic Modelling (Ord) (U01649)

? Credit Points : 10 ? SCQF Level : 9 ? Acronym : MAT-3-SMoO

Syllabus summary: 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.

Entry Requirements

? Pre-requisites : MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM, MAT-2-Prb or MAT-2-am3, MAT-2-mm3, MAT-2-am4, MAT-2-mm4, MAT-2-Prb or MAT-2-mi3, MAT-2-mi4

? Prohibited combinations : MAT-3-SMo

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Ordinary), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 3rd year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	09:00	09:50	KB
Lecture	Thursday	09:00	09:50	KB

Summary of Intended Learning Outcomes

The following are the learning objectives for the Honours version, MAT-3-SMo; for this (Ordinary) version there is more emphasis on the technical, rather than conceptual elements, which will be reflected by a different examination.

1. Ability to solve difference equations using generating functions, using P.S.+C.S.
2. Ability to classify states of a Markov Chain.
3. Ability to calculate mean first passage and recurrence times for an irreducible recurrent state Markov Chain.
4. Calculation of absorption probabilities for a Markov Chain with recurrent classes and transient states.
5. Understanding stationary and limiting behaviour and deriving these probability distributions.
6. Appreciating the range of applications, together with a facility to model appropriate problems in terms of a stochastic process.