Math 544    Fall 2005 

	       Stochastic Dynamics

          	Professor J. Duan  
		Tel: 312-567-5335
		E-mail: duan@iit.edu 
 
  Class Hours:   Tuesdays and Thursdays in E1 
  Office Hours:  Tuesdays and Thursdays  or by appointment
 
     This  course is about mathematical modeling by stochastic
differential equations and random dynamics.  It is specially
appropriate for graduate students who would like to use stochastic
methods in their research, or to learn such methods for long term
career development.

      We live in a world full of uncertainty.
Stochastic differential equations arise as models of random
phenomena in engineering and science. We will approach the subject
from  an applied point of view. Applications will be used
throughout the course to motivate and illustrate the concepts and
methods.
     

Topics include: 

   Basic Topics ---

Random variables   and Brownian motion (Wiener process);
stochastic continuity and mean-square convergence; stochastic
integrals; stochastic differential equations; numerical simulation
of stochastic differential equations; Ito's formula; Fokker-Planck
equation; exit/first passage problem.


   Additional topics ---

Dynamical behavior of  nonlinear systems arising from physical,
mechanical,electrical,chemical, and biological phenomena under
random influences; dynamical systems approach for stochastic differential
equations;   Lyapunov exponents  and ergodic theory; stochastic
bifurcation; phenomena induced by noise; impact of noise;
invariant manifold reduction of random systems; macroscopic
modeling of random systems.
 
Pre-requisite: Undergraduate course in Probability or Statistics, or consent of Instructor.
 
References:

   1. B. Oksendale: Stochastic Differential Equations
sixth Edition, September 2003

   2. Research articles from academic journals