J. Korean Math. Soc. 2005; 42(2): 269-289
Printed March 1, 2005
Copyright © The Korean Mathematical Society.
Youngmee Kwon and Hye-Jeong Kang
Hansung University, Seoul National University
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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