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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 4, Pages 764–768 (Mi tvp3779)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

Existence and uniqueness of a stationary solution of a nonlinear stochastic differential equation with memory

Yu. Yu. Bakhtin

International Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS

Abstract: The paper obtains sufficient conditions for the existence and uniqueness of a stationary solution of a nonlinear stochastic differential equation, a drift coefficient of which is a nonlinear functional of the history of the solution.

Keywords: stochastic differential equation with delay, Gibbs dynamics.

DOI: https://doi.org/10.4213/tvp3779

Full text: PDF file (555 kB)

English version:
Theory of Probability and its Applications, 2003, 47:4, 684–688

Bibliographic databases:

Received: 25.01.2002

Citation: Yu. Yu. Bakhtin, “Existence and uniqueness of a stationary solution of a nonlinear stochastic differential equation with memory”, Teor. Veroyatnost. i Primenen., 47:4 (2002), 764–768; Theory Probab. Appl., 47:4 (2003), 684–688

Citation in format AMSBIB
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\by Yu.~Yu.~Bakhtin
\paper Existence and uniqueness of a stationary solution of a nonlinear stochastic differential equation with memory
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 4
\pages 764--768
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\zmath{https://zbmath.org/?q=an:1054.60062}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 4
\pages 684--688
\crossref{https://doi.org/10.1137/S0040585X97980051}
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  • http://mi.mathnet.ru/eng/tvp3779
  • https://doi.org/10.4213/tvp3779
  • http://mi.mathnet.ru/eng/tvp/v47/i4/p764

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bakhtin Y., Mattingly J.C., “Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations”, Communications in Contemporary Mathematics, 7:5 (2005), 553–582  crossref  mathscinet  zmath  isi  scopus
    2. Gadat S., Panloup F., “Long Time Behaviour and Stationary Regime of Memory Gradient Diffusions”, Ann. Inst. Henri Poincare-Probab. Stat., 50:2 (2014), 564–601  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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