Title page for ETD etd-11152006-194212

Type of Document Dissertation
Author Wu, Jie
Author's Email Address wujie@math.lsu.edu
URN etd-11152006-194212
Title Limit Theorems for Weighted Stochastic Systems of Interacting Particles
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Padmanabhan Sundar Committee Chair
Ambar Sengupta Committee Member
George Cochran Committee Member
Jimmie Lawson Committee Member
Robert Perlis Committee Member
David Kirshner Dean's Representative
  • Interacting Particle Systems
  • Empirical Measures
  • Weak Convergence
  • SDE
  • SPDE
  • Stochastic Processes
Date of Defense 2006-11-08
Availability unrestricted

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 Iíve established are: (i) pathwise comparison of solutions, and (ii) compactness of support for the weak limit of the empirical measures.

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