** Topic: ** Mathematical Methods for Stochastic Models of Complex Networks

** Professor: **
Professor R. J. Williams, AP&M 7161.

** Time: ** Tu, Th 5-6.30pm.

** Place: ** AP&M 2402.

NOTE: There will be no class on Thu October 12, Tu October 24, Thu October 26. This class time is being made up with extra time for the other lectures and an additional make-up time.

** Office Hour: ** Thursdays, AP&M 7161, 11-11.45 a.m. and by appointment.

**
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 biological 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, especially to biological 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, stationary distributions for Markov processes, fluid models and reflected diffusion processes.

**
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).

** References: **

* Background References: *

* Biochemical Reaction Networks *

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

Last updated October 2, 2017.