DESCRIPTION
Diffusion processes arise in modelling a variety of random dynamic phenomena in the physical, biological, engineering and social sciences. They are also connected to the subject of partial differential equations. One method for constructing a large class of diffusions is via stochastic differential equations.

The book, Brownian Motion and Stochastic Calculus by I. Karatzas and S. Shreve, is used as a basis for this course. Topics to be covered include existence and uniqueness for stochastic differential equations and martingale problems, and sample applications. The course begins with a review of the necessary martingale theory and stochastic process terminology. Although stochastic calculus is not covered in depth, tutorials on this and weak convergence may be given as necessary to fill in background for the course participants.

MEETING TIME AND PLACE
MWF 2-3 p.m., Peterson Hall 102

PREREQUISITE
Math 280ABC or equivalent or consent of instructor.

TEXT
Karatzas, I. and Shreve, S., Brownian motion and stochastic calculus, 2nd edition, Springer, paperback. To be available at the start of Fall quarter in the Student Coop Bookstore.
Supplement on weak convergence: Chapter 3 of Ethier and Kurtz, Markov processes, to be available from Soft Reserves at the start of Fall quarter.

ENROLLMENT
Students wishing to attend this course are encouraged to enroll (at least on a S/U basis). (Enrollments in current courses are used as a basis for determining whether such courses will be offered in the future.) Students wishing to enroll for this course should register for Math 289A, Id. Number 266407 with Professor R. J. Williams.

Please note that Math 289 courses may be repeated for credit. These courses are generically labelled Topics in Probability and their content varies from year to year. In particular, the Math 289 courses for this year (1996-97) will be complementary to the Math 289A course offered last Spring.

QUESTIONS
Please direct any questions about the course to Professor Williams at williams@math.ucsd.edu or phone: 534-6446.

OTHER COURSES
Other topics in probability courses, are planned for the Winter and Spring of 1997. In particular, Professor Tom Kurtz will give a course on Measure Valued Diffusions:Fleming-Viot Processes in the Winter of 1997 and Professor Patrick Fitzsimmons will give a topics course in the Spring of 1997.