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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 2, Pages 400–409
DOI: https://doi.org/10.4213/tvp63 (Mi tvp63) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

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

P. N. Yarykin

M. V. Lomonosov Moscow State University
Full-text PDF (1063 kB) Citations (3)
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DOI: https://doi.org/10.4213/tvp63
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.
Received: 08.06.2005
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 2, Pages 387–396
DOI: https://doi.org/10.1137/S0040585X97982372
Bibliographic databases:
Document Type: Article
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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