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