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2010/1 Module Catalogue
 Module Code: MAT2003 Module Title: STOCHASTIC PROCESSES
Module Provider: Mathematics Short Name: MS238
Level: HE2 Module Co-ordinator: WULFF C Dr (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability
Assessment Pattern

                        Unit(s) of Assessment


                        Weighting Towards Module Mark( %)







Written examination – 2 hours, unseen





Qualifying Condition(s) 


An overall aggregate mark of 40% for the module.



Module Overview
This module introduces students to stochastic processes and its applications.
Module Aims
Realistic modelling of a real system very often requires the inclusion of probabilistic elements. A stochastic (as opposed to a deterministic) model will generally lead to more realistic predictions about the system. In this module we study a large class of stochastic processes, that is, probabilistic models for series of events.
Learning Outcomes
At completion of the module the students should have a thorough understanding of the properties of stochastic processes and be able to apply this knowledge to analyse specific stochastic processes, including biological, financial and engineering processes.
Module Content
Review of basic probability theory; concept of stochastic process; random walks; properties of Markov chains: recurrence and transience, periodicity, communicating classes, irreducibility; first step analysis; Basic Limit Theorem, existence proofs for stationary distributions, applications. Markov processes in continuous time: derivation of the Poisson process and generalised birth and death process.
Methods of Teaching/Learning

Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and background reading. Summary notes for the module are provided by the convener.

3 contact hours per week for 10 weeks 
Selected Texts/Journals

Recommended Reading


- Murray R. Spiegel, Schaum's outline of Calculus of Finite Differences


and Difference Equations (10th printing), McGraw-Hill Trade, (1994).


-H.M. Taylor and S. Karlin , An Introduction to Stochastic Modelling


(rev. ed.), Academic Press, (1994).



Further Reading


- G.P. Beaumont, Introductory Applied Probability, Ellis Horwood, (1983).


-W. Feller, An Introduction to Probability Theory and its Applications:


Vol. 1 (3rd ed.), Wiley, (1968).


- H.C. Tuckwell, Elementary Applications of Probability Theory, Chapman and Hall, (1995)
Last Updated
September 10