Limit Theorems for Weighted Stochastic Systems of Interacting Particles

• Main Author: Wu, Jie
• Other Authors: David Kirshner
• Format: Others
• Language: en
• Published: LSU 2006
• Subjects: Mathematics
• Online Access: http://etd.lsu.edu/docs/available/etd-11152006-194212/

The goal of this dissertation is to (a) establish the weak convergence of empirical measures formed by a system of stochastic differential equations, and (b) prove a comparison result and compactness of support property for the limit measure. The stochastic system of size n has coefficients that depend on the empirical measure determined by the system. The weights for the empirical measure are determined by a further n-system of stochastic equations. There is a random choice among N types of weights. The existence and uniqueness of solutions of the interacting system, weak convergence of the empirical measures, and the identification of the limit form the first part of this work. The second part deals with particular cases of interacting systems for which qualitative properties of the limit can be proved. The properties Ive established are: (i) pathwise comparison of solutions, and (ii) compactness of support for the weak limit of the empirical measures.