Geodesic
A~probabilistic representation of the solution of the directional derivative problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 172-176

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Let $\mathbf A$ be аn elliptic differential operator of the second order in a domain $D$ of an $N$-dimentional Euclidean space; $l$ be a smooth vector field on the boundary. A probabilistic representation for the solution of the boundary value problem $Au=0$, $\partial u/dl|_{\partial D}=f$ is given in terms of the local time on the boundary. The central limit theorem is proved for a functional of the type of the local time on the boundary. 
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     author = {A. P. Korostelev},
     title = {A~probabilistic representation of the solution of the directional derivative problem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {172--176},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a14/}
}
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A. P. Korostelev. A~probabilistic representation of the solution of the directional derivative problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 172-176. http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a14/