Unit information: Intoduction To Stochastic Analysis in 2013/14

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 (MATH35700) [includes: Applied Probability 2 (MATH21400)] Measure Theory and Integration (MATH34000) [includes: Metric Spaces (MATH20200)] Functional Analysis 3 (MATH36202) [includes: Metric Spaces (MATH20200)]
Co-requisites	None.
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

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 on 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.

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.

Further information can be found at: http://www.maths.bris.ac.uk/study/undergrad/

Intended Learning Outcomes

To gain profound understanding of the basic notions and techniques of the theory of:

• Brownian motion;
• stochastic integration;
• 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.

Teaching Information

Lectures supported by problem sheets and solution sheets.

Assessment Information

• The final assessment mark will be calculated as follows: 20% based on home works + 80% based on final 2.5 hour exam

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

• F. Klebaner: Introduction to Stochastic Calculus With Applications, World Scientific, 2005

• 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

• Instructor’s lecture notes and problem sheets