Introduction to Stochastic Analysis
The unit aims to give a rigorous yet non-technical introduction to Brownian motion, with an emphasis on concrete calculations and examples.
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.
- 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
- 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
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.
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.
Further exam information can be found on the Maths Intranet.