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Unit information: Stochastic Processes in 2015/16

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

Unit name Stochastic Processes
Unit code MATHM6006
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1B (weeks 7 - 12)
Unit director Professor. Balint Toth
Open unit status Not open

MATH21400 Applied Probability 2 essential. Background in PDE's helpful but not essential



School/department School of Mathematics
Faculty Faculty of Science

Description including Unit Aims

Unit aims

The aim of the unit is to introduce theory of Brownian motions, in particular, how to construct it from random walks, various properties, and finally stochastic integration leading to a brief survey of diffusion processes.

General Description of the Unit

This unit aims for an intuitive understanding of Brownian motion and stochastic calculus, although rigorous proofs will be presented for a few of the most beautiful results. Students should be comfortable with reading and understanding rigorous proofs. Understanding Brownian motion, commonly regarded as the canonical example of a martingale and a Markov process with continuous paths, is essential for any future study of stochastic processes and its applications.


Relation to Other Units

This unit is a first course in continuous time stochastic processes and introductory stochastic analysis.

Intended Learning Outcomes

Learning Objectives

At the end of the unit students should:

  • be able to recall all definitions and main results,
  • be able to understand on an intuitive level the reasoning behind proofs of major results,
  • be able to apply the theory in standard situations,
  • be able to use the ideas of the unit in unseen situations

Transferable Skills

Understanding the behaviour of diffusion processes so as to be able to use them (e.g. perform calculations and write simulations) in problems arising in physics, engineering, financial calculus or statistics.

Teaching Information

Lectures supported by problem sheets and solution sheets.

Assessment Information

100% Examination.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

Reading and References

Geoffrey R. Grimmett and David R. Stirzaker, Probability and Random Processes, Oxford University Press, 3rd edition can be used as the main reference on Brownian motion. (selected chapters)

B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, 6th edition can be used as a reference for stochastic integration. (selected chapters)

Hand written lecture notes available online at the course web page.