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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 2, Pages 400–409 (Mi tvp63)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Stability of the nonlinear stochastic process approximizing a system of interacted particles

P. N. Yarykin

M. V. Lomonosov Moscow State University

Abstract: The nonlinear SDE of McKean–Vlasov type in the absence of external fields is considered. First, the existence and the uniqueness of the equation solution are proved. Next, the existence and the uniqueness of the stationary solution at the class of probability with fixed expectation are proved. Also, weak convergence to invariant probability is proved.

Keywords: nonlinear stochastic process, McKean–Vlasov equation, stability.

DOI: https://doi.org/10.4213/tvp63

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English version:
Theory of Probability and its Applications, 2007, 51:2, 387–396

Bibliographic databases:

Received: 08.06.2005

Citation: P. N. Yarykin, “Stability of the nonlinear stochastic process approximizing a system of interacted particles”, Teor. Veroyatnost. i Primenen., 51:2 (2006), 400–409; Theory Probab. Appl., 51:2 (2007), 387–396

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. N. Yarykin, “The behaviour of a non-linear random process in a neighbourhood of its stationary distributions”, Russian Math. Surveys, 61:4 (2006), 788–790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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