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Teoriya Veroyatnostei i ee Primeneniya, 1963, Volume 8, Issue 1, Pages 80–87
(Mi tvp4649)
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This article is cited in 20 scientific papers (total in 20 papers)
Short Communications
Diffusion Processes with Reflection and a Third Boundary Value Problem
M. I. Freidlin Moscow
Abstract:
In this paper a Markov diffusion process with reflection on the boundary of a differentiable manifold is constructed. This construction enables us to investigate the boundary value problem: $\sum\limits_{i,j=1}^n{a_{ij}(x)\frac{{\partial^2 u}}{{\partial x^i\partial x^j}}+}\sum\limits_{i=1}^n{b_i(x)}\frac{{\partial u}}{{\partial x^i}}=f(x),\quad\left.{\frac{{\partial u}}{{\partial l}}}\right|_\Gamma=0,$ using probability methods. Neumann’s problem is a special case of this problem (when $l$ is conformal to the boundary).
Received: 31.05.1961
Citation:
M. I. Freidlin, “Diffusion Processes with Reflection and a Third Boundary Value Problem”, Teor. Veroyatnost. i Primenen., 8:1 (1963), 80–87; Theory Probab. Appl., 8:1 (1963), 75–83
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Abstract page: | 187 | Full-text PDF : | 105 |
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