Program
Propagation of chaos for stochastic interacting particle system
Student No.:50
Time:Tue/Thu 10:10-12:00, 2014-07-17 ~ 2014-08-14
Instructor:Jian-Guo Liu  [Duke University]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2014-7-17
Ending Date:2014-8-14
 

Description:

 

 
In this short course, I will present the basic idea on the rigorous derivation of the (kinetic) continuum limit for some important stochastic interacting particle systems in physics and biology.
 
We prove propagation of chaos for these for these interacting particle systems. There is no prerequisite on the knowledge of stochastic differential equation and kinetic theory. I will give a quick introduction on all needed basic tools.
 

The topics include: 

(1) Stochastic differential equation basic, stopping time, martingale

(2) Basic PDE theory for the mean field equations

(3) Propagation of chaos for 2D stochastic vortex system and convergence to the Navier-Stokes equation

(4) Propagation of chaos of stochastic interacting particle system with Newtonian potential 

(5) Propagation of chaos and convergence to the keller-segel equation.

 

 
 
Reference:
 

[1] B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 6th edition, 2010

[2] A. S. Sznitman, Topics in propagation of chaos, Springer 1991

[3] J.-G. Liu and R. Yang, Propagation of chaos of stochastic interacting particle system with Newtonian potential (in preparation) 

[4] M Hauray and S Mischler, On Kac’s chaos and related problems, arXiv:1205.4518