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Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions

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  • Hitsuda, Masuyuki
  • Mitoma, Itaru

Abstract

The central limit (or fluctuation) phenomena are discussed in the interacting diffusion system. The tightness in the Kolmogorov-Prokhorov sense is proved for a sequence of distribution valued processes arising from finite particle systems. Further, the stochastic differential equation for the limit process is derived by constructing an infinite dimensional Brownian motion.

Suggested Citation

  • Hitsuda, Masuyuki & Mitoma, Itaru, 1986. "Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 311-328, August.
    • Handle: RePEc:eee:jmvana:v:19:y:1986:i:2:p:311-328
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    Cited by:

    1. Fernandez, Begoña & Méléard, Sylvie, 1997. "A Hilbertian approach for fluctuations on the McKean-Vlasov model," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 33-53, October.
    2. Chevallier, Julien & Ost, Guilherme, 2020. "Fluctuations for spatially extended Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5510-5542.
    3. Kurtz, Thomas G. & Xiong, Jie, 1999. "Particle representations for a class of nonlinear SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 103-126, September.
    4. Jie Xiong & Yong Zeng, 2011. "A branching particle approximation to a filtering micromovement model of asset price," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 111-140, May.

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