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Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 172–176 (Mi tvp2691)  

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

Short Communications

A probabilistic representation of the solution of the directional derivative problem

A. P. Korostelev

Moscow

Abstract: Let $\mathbf A$ be аn elliptic differential operator of the second order in a domain $D$ of an $N$-dimentional Euclidean space; $l$ be a smooth vector field on the boundary. A probabilistic representation for the solution of the boundary value problem $Au=0$, $\partial u/dl|_{\partial D}=f$ is given in terms of the local time on the boundary. The central limit theorem is proved for a functional of the type of the local time on the boundary.

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English version:
Theory of Probability and its Applications, 1973, 18:1, 169–172

Bibliographic databases:

Received: 14.10.1971

Citation: A. P. Korostelev, “A probabilistic representation of the solution of the directional derivative problem”, Teor. Veroyatnost. i Primenen., 18:1 (1973), 172–176; Theory Probab. Appl., 18:1 (1973), 169–172

Citation in format AMSBIB
\Bibitem{Kor73}
\by A.~P.~Korostelev
\paper A~probabilistic representation of the solution of the directional derivative problem
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 1
\pages 172--176
\mathnet{http://mi.mathnet.ru/tvp2691}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=312571}
\zmath{https://zbmath.org/?q=an:0299.60049}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 18
\issue 1
\pages 169--172
\crossref{https://doi.org/10.1137/1118015}


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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. S. V. Nagaev, V. I. Vakhtel', “Limit theorems for probabilities of large deviations of a Galton-Watson process”, Discrete Math. Appl., 13:1 (2003), 3–27  mathnet  crossref  mathscinet  zmath
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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