On Boundary Conditions For Multidimensional Diffusion Processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 2, pp. 172-185
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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.
@article{TVP_1959_4_2_a3,
author = {A. D. Venttsel'},
title = {On {Boundary} {Conditions} {For} {Multidimensional} {Diffusion} {Processes}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {172--185},
publisher = {mathdoc},
volume = {4},
number = {2},
year = {1959},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1959_4_2_a3/}
}
A. D. Venttsel'. On Boundary Conditions For Multidimensional Diffusion Processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 2, pp. 172-185. http://geodesic.mathdoc.fr/item/TVP_1959_4_2_a3/