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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 1, Pages 156–161 (Mi tvp306)  

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

Short Communications

Limit theorem for one-dimensional stochastic equations

S. Ya. Makhno

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: One-dimensional stochastic equations are considered whose coefficients depend on a small parameter. Necessary and sufficient conditions are obtained for the weak convergence of their solutions to the solution of the stochastic equation containing local time of an unknown process.

Keywords: stochastic equations, local time, necessary conditions of convergence, sufficient conditions of convergence.

DOI: https://doi.org/10.4213/tvp306

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English version:
Theory of Probability and its Applications, 2004, 48:1, 164–169

Bibliographic databases:

Received: 30.05.2000

Citation: S. Ya. Makhno, “Limit theorem for one-dimensional stochastic equations”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 156–161; Theory Probab. Appl., 48:1 (2004), 164–169

Citation in format AMSBIB
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\by S.~Ya.~Makhno
\paper Limit theorem for one-dimensional stochastic equations
\jour Teor. Veroyatnost. i Primenen.
\yr 2003
\vol 48
\issue 1
\pages 156--161
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\zmath{https://zbmath.org/?q=an:1055.60060}
\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 1
\pages 164--169
\crossref{https://doi.org/10.1137/S0040585X980191}
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  • https://doi.org/10.4213/tvp306
  • http://mi.mathnet.ru/eng/tvp/v48/i1/p156

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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. Sergey Ya. Makhno, Irina A. Yerisova, “Limit theorems for backward stochastic equations”, Theory Stoch. Process., 14(30):2 (2008), 93–107  mathnet
    2. Ivan H. Krykun, “Large deviation principle for stochastic equations with local time”, Theory Stoch. Process., 15(31):2 (2009), 140–155  mathnet  mathscinet  zmath
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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