Fluctuations in a Markovian system of pairwise interacting particles
type: Item
instance of: scholarly article
title: Fluctuations in a Markovian system of pairwise interacting particles
zbMATH Open document ID: 0635.60092
DOI: 10.1007/BF00320923
publication date: 1988-01-01T00:00:00Z
review text: 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 have 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 \textit{H. Tanaka} [Stochastic analysis, Proc. Taniguchi Int. Symp., Katata \& Kyoto/Jap. 1982, North- Holland Math. Libr. 32, 469-488 (1984; Zbl 0552.60051)].
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4034820
zbMATH Keywords: master equation
zbMATH Keywords: Boltzmann equation
zbMATH Keywords: Cameron-Martin formula
zbMATH Keywords: two-speed gas model
zbMATH Keywords: variance functional for fluctuations
author: Kohei Uchiyama
MaRDI profile type: Publication
cites work: Q3236483
cites work: A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
cites work: Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated
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cites work: Q3711424
cites work: Fluctuations of Markovian systems in Kac's caricature of a Maxwellian gas
cites work: Q3036445
cites work: Q3775374
full work available at URL: https://doi.org/10.1007/bf00320923
OpenAlex ID: W2072680482
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4034820