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 via potential theory. Rather than describing the general theory without a context, this course will describe some of the properties and potential applications of diffusions through the concrete example of reflecting Brownian motions and applications to queueing networks. (Queueing networks are of current relevance for modelling communication networks and manufacturing systems.) Some aspects of the auxiliary topics of Markov processes, weak convergence in path space, and applications of stochastic calculus will also be discussed.

PREREQUISITES
A first graduate course in probability is highly recommended (e.g., Math 280). Those who do not have a background in Brownian motion, continuous martingales or stochastic calculus may wish to attend the last three weeks of Math 280B and at least the first part of Math 280C, when these subjects will be discussed there.

FIRST MEETING
The first meeting will be in HSS 2152 on Monday, April 1 at 11 a.m. Future meetings may be held at a different time. This will be discussed at the first meeting. Students interested in the course are asked to indicate their interest to Professor Williams by sending email to williams@math.ucsd.edu. Questions may also be directed to this address.