INITIAL BOUNDARY VALUE PROBLEMS IN A BOUNDED DOMAIN: PROBABILISTIC REPRESENTATIONS OF SOLUTIONS AND LIMIT THEOREMS II

被引：2

作者：

Ibragimov, I. A. ^{[1
,2
]}

Smorodina, N., V ^{[1
,2
]}

Faddeev, M. M. ^{[2
]}

机构：

[1] Russian Acad Sci, St Petersburg Dept Steklov Math Inst, St Petersburg 191023, Russia

[2] St Petersburg State Univ, St Petersburg 199034, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2018年 / 62卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

initial-boundary value problems; evolution equations; Schrodinger equation; limit theorems; Skorokhod problem; Feynman integral; Feynman measure;

D O I：

10.1137/S0040585X97T98868X

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 Schrodinger equation) in a bounded subdomain of 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.

引用

页码：356 / 372

页数：17

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