| Unit name | Intoduction To Stochastic Analysis |
|---|---|
| Unit code | MATHM0017 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Balint Toth |
| Open unit status | Not open |
| Pre-requisites |
Any two of the following three: Probability 3 (MATH 35700) [includes: Applied Probability 2 (MATH 21400)] Measure Theory and Integration (MATH 34000) [includes: Metric Spaces (MATH 20200)] Functional Analysis 3 (MATH 36202) [includes: Metric Spaces (MATH 20200)] |
| Co-requisites |
None. |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit aims
The aim of the unit is to introduce theory of Brownian motion, continuous martingales, stochastic integration, stochastic differential equations and diffusion processes. With particular emphasis on applications to physical sciences, financial mathematics and other branches of applied mathematics.
General Description of the Unit
The course is intended for (post)graduate students of pure and applied mathematics with a sufficiently strong background in analysis. Construction and analytic properties of Brownian motion, stochastic integration a la Ito, 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. The course is recommended to all mathematics (post)graduate students with a broad view.
Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/
Learning Objectives
To gain profound 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 the postgraduate student for independent research in mathematics.
Lectures supported by problem sheets and solution sheets.
80% Examination and 20% Coursework.
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.
