Geodesic
Initial-boundary value problems in a~bounded domain: probabilistic representations of solutions and limit theorems.~II
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 3, pp. 446-467

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The paper puts forward a new method of construction of a probabilistic representation of solutions to initial-boundary value problems for a number of evolution equations (in particular, for the Schrödinger equation) in a bounded subdomain of $\mathbb R^2$ with smooth boundary. Our method is based on the construction of a special extension of the initial function from the domain to the entire plane. For problems with Neumann boundary condition, this method produces a new approach to the construction of a Wiener process “reflected from the boundary,” which was first introduced by A. V. Skorokhod.
Keywords: initial-boundary value problems, Schrödinger equation, limit theorems, Skorokhod problem, Feynman integral, Feynman measure.
Mots-clés : evolution equations 
@article{TVP_2017_62_3_a1,
     author = {I. A. Ibragimov and N. V. Smorodina and M. M. Faddeev},
     title = {Initial-boundary value problems in a~bounded domain: probabilistic representations of solutions and limit {theorems.~II}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {446--467},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_3_a1/}
}
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I. A. Ibragimov; N. V. Smorodina; M. M. Faddeev. Initial-boundary value problems in a~bounded domain: probabilistic representations of solutions and limit theorems.~II. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 3, pp. 446-467. http://geodesic.mathdoc.fr/item/TVP_2017_62_3_a1/