Standard

Initial boundary value problems in a bounded domain : Probabilistic representations of solutions and limit theorems II. / Ibragimov, I. A.; Smorodina, N. V.; Faddeev, M. M.

в: Theory of Probability and its Applications, Том 62, № 3, 01.01.2018, стр. 356-372.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Ibragimov, IA, Smorodina, NV & Faddeev, MM 2018, 'Initial boundary value problems in a bounded domain: Probabilistic representations of solutions and limit theorems II', Theory of Probability and its Applications, Том. 62, № 3, стр. 356-372. https://doi.org/10.1137/S0040585X97T98868X

APA

Ibragimov, I. A., Smorodina, N. V., & Faddeev, M. M. (2018). Initial boundary value problems in a bounded domain: Probabilistic representations of solutions and limit theorems II. Theory of Probability and its Applications, 62(3), 356-372. https://doi.org/10.1137/S0040585X97T98868X

Vancouver

Ibragimov IA, Smorodina NV, Faddeev MM. Initial boundary value problems in a bounded domain: Probabilistic representations of solutions and limit theorems II. Theory of Probability and its Applications. 2018 Янв. 1;62(3):356-372. https://doi.org/10.1137/S0040585X97T98868X

Author

Ibragimov, I. A. ; Smorodina, N. V. ; Faddeev, M. M. / Initial boundary value problems in a bounded domain : Probabilistic representations of solutions and limit theorems II. в: Theory of Probability and its Applications. 2018 ; Том 62, № 3. стр. 356-372.

BibTeX

@article{c410326aaf584f05a7f56f1e6058ea17,
title = "Initial boundary value problems in a bounded domain: Probabilistic representations of solutions and limit theorems II",
abstract = "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 Schr{\"o}dinger equation) in a bounded subdomain of ℝ2 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 = "Evolution equations, Feynman integral, Feynman measure, Initial-boundary value problems, Limit theorems, Schr{\"o}dinger equation, Skorokhod problem, Schrodinger equation, initial-boundary value problems, limit theorems, evolution equations",
author = "Ibragimov, {I. A.} and Smorodina, {N. V.} and Faddeev, {M. M.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1137/S0040585X97T98868X",
language = "English",
volume = "62",
pages = "356--372",
journal = "Theory of Probability and its Applications",
issn = "0040-585X",
publisher = "Society for Industrial and Applied Mathematics",
number = "3",

}

RIS

TY - JOUR

T1 - Initial boundary value problems in a bounded domain

T2 - Probabilistic representations of solutions and limit theorems II

AU - Ibragimov, I. A.

AU - Smorodina, N. V.

AU - Faddeev, M. M.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 ℝ2 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.

AB - 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 ℝ2 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.

KW - Evolution equations

KW - Feynman integral

KW - Feynman measure

KW - Initial-boundary value problems

KW - Limit theorems

KW - Schrödinger equation

KW - Skorokhod problem

KW - Schrodinger equation

KW - initial-boundary value problems

KW - limit theorems

KW - evolution equations

UR - http://www.scopus.com/inward/record.url?scp=85052757657&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T98868X

DO - 10.1137/S0040585X97T98868X

M3 - Article

AN - SCOPUS:85052757657

VL - 62

SP - 356

EP - 372

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 3

ER -

ID: 35401281