Introduction to Stochastic Analysis

Unit aims

The unit aims to give a rigorous yet non-technical introduction to Brownian motion, with an emphasis on concrete calculations and examples.

Unit description

The course is intended for Master's students with a sufficiently strong background in analysis. Construction and analytic properties of Brownian motion, stochastic integration, stochastic differential equations and their strong and weak solutions, various approaches to diffusion processes will be covered. These are all topics of central importance in the general advanced mathematical culture. Special emphasis will be put on various applications of the theory.

Relation to other units

This is a new unit for 2018/19. 

Learning objectives

  • To gain a good understanding of the basic notions and techniques of the theory of:
    • Brownian motion;
    • Stochastic differential equations and their strong and weak solutions;
    • Diffusion processes;
    • Applications of these concepts.
  • To prepare students for independent research in mathematics.

Reading and References

Recommended:

  • K.L. Chung, R. Williams: Introduction to stochastic integration. Second edition. Birkauser, 1989
  • I. Karatzas, S. Shreve: Brownian Motion and Stochastic Calculus, Springer 1991
  • J. Lamperti, Stochastic Processes: a Survey of the Mathematical Theory, Springer 1977
  • B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 6th edition, Springer 2010

Unit code: MATHM0017
Level of study: M/7 
Credit points: 20
Teaching block (weeks): 1 (1-12)
Lecturer: Dr Feng Yu

Pre-requisites

Either a) MATH30006 Further Topics in Probability 3 or b) MATH20008 Probability 2 and MATH30007 Measure Theory and Integration.

From 2019/20 onwards, MATH20402 Applied Partial Differential Equations 2 will also be a prerequisite.

Co-requisites

None

Methods of teaching

Lectures, regular formative problem sheets and office hours

Methods of Assessment

The pass mark for this unit is 50.

The final mark is calculated as follows:

  • 100% Exam

NOTE: Calculators are NOT allowed.

For information resit arrangements, please see the re-sit page on the intranet.

Please use these links for further information on relative weighting and marking criteria.

Further exam information can be found on the Maths Intranet.

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