A CLASS OF NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS(SDES) WITH JUMPS DERIVED BY PARTICLE REPRESENTATIONS

Abstract

An in¯nite system of stochastic di??erential equations(SDE)driven by Brownian motions and compensated Poisson ran-dom measures for the locations and weights of a collection of par-ticles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted mea-sure V , which is shown to be a solution of a stochastic di??erential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.