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 |
Pre-requisites |
MATH36204 Martingale Theory and Applications 3 or MATHM6204 Martingale Theory and Applications 4. Background in PDE's helpful but not essential |
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 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.
COURSE WEB PAGE: http://www.bristol.ac.uk/maths/study/undergraduate/units1617/levelm7units/stochasticprocesses/
Relation to Other Units
This unit is a first course in continuous time stochastic processes and introductory stochastic analysis.
Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
Learning Objectives
At the end of the unit students should:
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.
Lectures supported by problem sheets and solution sheets.
80% Examination
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.
Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html