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Fluctuations in a Markovian system of pairwise interacting particles
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  • Published: September 1988

Fluctuations in a Markovian system of pairwise interacting particles

  • Kōhei Uchiyama1 

Probability Theory and Related Fields volume 79, pages 289–302 (1988)Cite this article

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  • 7 Citations

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Summary

Analogously to the Kac's master equation approach to the spatially homogeneous Boltzmann equation we introduce a system of Markov processes of many particles moving on a countable set with pairwise interaction, and investigate the fluctuation around McKean's non-linear limit process. Our model possibly admits simultaneous jumps of two particles, which make impossible both such characterizations of the fluctuation in the limit and techniques (based on the Cameron-Martin formula) as has previously been obtained or used for diffusion models and for McKean's two-speed gas model. We obtain a new description of the variance functional for the fluctuation, and, by applying it in the case of no simultaneous jumps, give a new derivation of a formula of H. Tanaka [7].

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References

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Authors and Affiliations

  1. Department of Mathematics, Hiroshima University, 730, Hiroshima, Japan

    Kōhei Uchiyama

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  1. Kōhei Uchiyama
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Uchiyama, K. Fluctuations in a Markovian system of pairwise interacting particles. Probab. Th. Rel. Fields 79, 289–302 (1988). https://doi.org/10.1007/BF00320923

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  • Received: 23 June 1986

  • Revised: 26 April 1988

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00320923

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Keywords

  • Stochastic Process
  • Probability Theory
  • Markov Process
  • Diffusion Model
  • Boltzmann Equation
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