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Teoriya Veroyatnostei i ee Primeneniya, 1959, Volume 4, Issue 2, Pages 172–185 (Mi tvp4877)  

This article is cited in 203 scientific papers (total in 204 papers)

On Boundary Conditions For Multidimensional Diffusion Processes

A. D. Venttsel'

Moscow
Abstract: The problem considered in the paper is as follows: given an elliptical operator $\mathfrak{A}$ in a closed bounded region $K$, the most general boundary conditions are sought, which restrict $\mathfrak{A}$ to an infinite-simal operator of a Markov process in $K$. This problem is solved for the case when $K$ is a circle or a sphere and only for processes invariant by rotations. In the general case when a process is given, boundary conditions are found, which are satisfied by all smooth functions in the domain of the infinitesimal operator of the process; however, it is not known whether this domain can be constructed from the boundary conditions.
Received: 24.11.1958
English version:
Theory of Probability and its Applications, 1959, Volume 4, Issue 2, Pages 164–177
DOI: https://doi.org/10.1137/1104014
Document Type: Article
Language: Russian
Citation: A. D. Venttsel', “On Boundary Conditions For Multidimensional Diffusion Processes”, Teor. Veroyatnost. i Primenen., 4:2 (1959), 172–185; Theory Probab. Appl., 4:2 (1959), 164–177
Citation in format AMSBIB
\Bibitem{Ven59}
\by A.~D.~Venttsel'
\paper On Boundary Conditions For Multidimensional Diffusion Processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1959
\vol 4
\issue 2
\pages 172--185
\mathnet{http://mi.mathnet.ru/tvp4877}
\transl
\jour Theory Probab. Appl.
\yr 1959
\vol 4
\issue 2
\pages 164--177
\crossref{https://doi.org/10.1137/1104014}
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  • This publication is cited in the following 204 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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