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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 160–163 (Mi tvp2689)

Short Communications

Boundary behaviour of conditional diffusion processes

Yu. I. Kifer

Moscow

Abstract: Let $G$ be a bounded domain in $R^n$ of class $A^{(2)}$ with the boundary $\Gamma$, and $x_t$ be a diffusion process in $G$ with absorption on $\Gamma$. Denote by $q(x,\gamma)$ the distribution density of the exit point of $x_t$ on $\Gamma$, and let $\widehat x_t$ be the conditional process given that $x_t$ is absorbed at a point $o$.
In the paper, the behaviour of the function $q(x,o)$ as $x\to o$ and of the process $\widehat x_t$ near $o$ is studied.

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English version:
Theory of Probability and its Applications, 1973, 18:1, 158–161

Bibliographic databases:

Citation: Yu. I. Kifer, “Boundary behaviour of conditional diffusion processes”, Teor. Veroyatnost. i Primenen., 18:1 (1973), 160–163; Theory Probab. Appl., 18:1 (1973), 158–161

Citation in format AMSBIB
\Bibitem{Kif73} \by Yu.~I.~Kifer \paper Boundary behaviour of conditional diffusion processes \jour Teor. Veroyatnost. i Primenen. \yr 1973 \vol 18 \issue 1 \pages 160--163 \mathnet{http://mi.mathnet.ru/tvp2689} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=310984} \zmath{https://zbmath.org/?q=an:0303.60069} \transl \jour Theory Probab. Appl. \yr 1973 \vol 18 \issue 1 \pages 158--161 \crossref{https://doi.org/10.1137/1118013}