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

  • KWON YOUNGMEE (Department of Computer Science Hansung Univ.) ;
  • KANG HYE-JEONG (SRCCS, Seoul National Univ.)
  • Published : 2005.02.01

Abstract

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

References

  1. S. N. Ethier and T. G. Kurtz, Markov processes:Characterization and convergence, Wiely, New York, 1986
  2. T. G. Kurtz, Averaging for martingale problems and stochastic application, Lecture notes in Control Inform 177 (1992), 186-209 https://doi.org/10.1007/BFb0007058
  3. H. P. McKean, Propagation of chaos for a class of nonlinear parabolic equations., Lecture series in Differential Equations 2 (1967), 177-194
  4. T. G. Kurtz and J. Xiong, Particle representations for a class of nonlinear SPDEs, Stochastic Process. Appl. 83 (1999), 103-126 https://doi.org/10.1016/S0304-4149(99)00024-1