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2010/1 Module Catalogue
Module Provider: Mathematics Short Name: MS334
Level: HE3 Module Co-ordinator: MELBOURNE I Prof (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability


Assessment Pattern

Unit(s) of Assessment
Weighting Towards Module Mark( %)
Coursework: the form of exercises and class tests
Exam: Written examination (2 hours, unseen).

Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass the module.

Module Overview

The module introduces Brownian motion, related continuous time, continuous state space stochastic processes and processes with independent and stationary increments.

Stochastic Processes (required), Mathematical Statistics (desirable)
Module Aims

Learning Outcomes

At the end of the module a student should be able to:



(1)               define Brownian motion and related processes and calculate associated probabilities


(2)               construct and analyse processes with independent and stationary increments


(3)        define and apply martingales in continuous time.
Module Content

Continuous time and state space models. Processes with independent and stationary increments. Brownian motion, reflection principle, recurrence, relation to random walks. Geometric Brownian motion.   Irregularity of Brownian Motion.   General Gaussian processes, Brownian bridge, Ornstein-Uhlenbeck process.  Martingales, maximal inequality,  filtrations, stopping times.

Methods of Teaching/Learning

3 contact hours per week for 10 weeks. Teaching is by lectures and tutorials.  Learning takes place through lectures, tutorials, exercises and background reading.

Selected Texts/Journals



H M Taylor and S. Karlin , An introduction to stochastic modelling, 3rd ed, Academic Press, (1998)



Further Reading


G R Grimmett and D Stirzaker, Probability and Random Processes, 2nd ed, Clarendon 1992


R S Pindyck and D L Rubinfeld, Econometric Models and Economic Forecasts, McGraw-Hill (1998)


Core Reading for Subject 103, Institute and Faculty of Actuaries (1999).

Last Updated

September 10