Geodesic
Diffusion Processes with Reflection and a Third Boundary Value Problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 1, pp. 80-87

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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). 
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     author = {M. I. Freidlin},
     title = {Diffusion {Processes} with {Reflection} and a {Third} {Boundary} {Value} {Problem}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     volume = {8},
     number = {1},
     year = {1963},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1963_8_1_a5/}
}
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M. I. Freidlin. Diffusion Processes with Reflection and a Third Boundary Value Problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 1, pp. 80-87. http://geodesic.mathdoc.fr/item/TVP_1963_8_1_a5/