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Instructor: Bruce Driver (driver@math.ucsd.edu), AP&M 7414, 534-2648.   Office Hours:  TBA

TA:  There will be no TA for this course.

Meeting times: Lectures are on MWF 11:00a - 11:50a in AP&M 6218.

Textbook: Introduction to Stochastic Integration, K. L. Chung and R. J. Williams, 2nd edition. There may also be some extra notes which will be distributed on this web-page at "Lecture Notes."

Prerequisites: Math 280A-B or consent of the instructor.

Homework: There will be a few home works throughout the quarter.

Grading: Final Grade = homework and attendance.

Description:  Stochastic differential equations (SDE) can be used to model a variety of random dynamic phenomena in the physical, biological, engineering and social sciences. Solutions of these equations are often Markov diffusion processes. Because of this SDE theory has strong links to the classical theory of partial differential equations (PDE).

Stochastic differential equations arise in modeling a variety of random dynamic phenomena in the physical, biological, engineering and social sciences. Solutions of these equations are often diffusion processes and hence are connected to the subject of partial differential equations. This course will present the basic theory of stochastic differential equations and provide examples of its application.

Topics:

1.  A review of the relevant stochastic process and martingale theory.
2. Stochastic calculus including Ito's formula.
3. Existence and uniqueness for stochastic differential equations, strong Markov property.
4. Applications.

RECOMMENDED ADDITIONAL REFERENCES:

1. Karatzas, I. and Shreve, S., Brownian motion and stochastic calculus, 2nd edition, Springer.
2. Oksendal, B., Stochastic Differential Equations, Springer, 5th edition, 1998.
3. Lawrence C. Evans, An Introduction To Stochastic Differential Equations Version 1.2

OTHER REFERENCES:

1. Metivier, M., Semimartingales, de Gruyter, Berlin, 1982.
2. Protter, P., Stochastic Integration and Differential Equations, Springer.
3. Revuz, D., and Yor, M., Continuous Martingales and Brownian Motion, Springer, Third Edition, 1999.
4. Rogers, L. C. G., and Williams, D., Diffusions, Markov Processes, and Martingales, Wiley, Volume 1: 1994, Volume 2: 1987.
5. Jacod, J., and Shiryaev, A. N., Limit theorems for stochastic processes, Springer-Verlag, 1987.

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Last modified on Tuesday, 25 March 2008 10:35 AM.