** Topic: ** Stochastic Models of Complex Networks

** Professor: **
Professor R. J. Williams, AP&M 6121.

** Time: ** MW noon-1.20pm.

** Place: ** AP&M 6218.

** Office Hours: ** MW 4-5pm

NO CLASS OCTOBER 6, 8, 13.

**
Background: **
Stochastic models of complex networks arise in a wide variety of applications
in science and engineering.
Specific instances include high-tech manufacturing, telecommunications,
computer systems, service systems and biochemical reaction networks.
There are challenging mathematical problems stemming from the need to
analyse and control such networks.

**
Content: **
This course will describe some general mathematical techniques for
modeling stochastic networks, for deriving approximations at various
scales (especially deterministic differential equation and diffusion
approximations), and for analyzing the behavior of these models.
Applications to queueing networks and biochemical reaction networks
will be used to illustrate the concepts developed.

The mathematical topics covered will include path spaces for stochastic processes, weak convergence of processes, fundamental building block processes and invariance principles, quasireversibility and stationary distributions for Markov processes, and others.

**
Prerequisites: **
This is an advanced graduate probability course featuring a topic of
current research interest. Students enrolling in this course should
have a background in probability at the level of Math 280AB
(courses such as Math 285, Math 280C, Math 286
provide additional useful background).

** First class meeting: ** AP&M 5402, noon-12.50pm

The first class meeting will be an organizational meeting. It will be
held on Friday, September 26 at noon.
The regular class meeting time will be decided at that meeting.
(Most likely the class will meet once per
week for 2.5 hours or twice a week for 80 minutes per class.
Wednesday or Thursday afternoons are possible good candidates, but they are
not the only possibilities.).

If you are interested in enrolling in the class, please send email to Professor Williams at "williams at math dot ucsd dot edu" indicating what times you are NOT available to attend class. This is especially important if you cannot attend the organizational meeting. (There will be no class between October 4 and October 14, inclusive).

**
Assessment: **
Students enrolled in the course will make in-class presentations on
topics related to the course.

** References: **

* Background References: *

* Papers: *

** Questions: ** Please direct any questions to
Professor Williams (williams at math dot ucsd dot edu).

Last updated April 9, 2009.