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J. Korean Math. Soc. 2005; 42(2): 269-289

Printed March 1, 2005

Copyright © The Korean Mathematical Society.

A class of nonlinear stochastic differential equations(SDEs) with jumps derived by particle representations

Youngmee Kwon and Hye-Jeong Kang

Hansung University, Seoul National University

Abstract

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An infinite system of stochastic differential equations (SDE) driven by Brownian motions and compensated Poisson random measures for the locations and weights of a collection of particles 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 measure $V$, which is shown to be a solution of a stochastic differential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.

Keywords: SDE, Poisson random measure, weak convergence

MSC numbers: Primary 60H10, 60H15; Secondary 60G57

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