PROBABILISTIC-INTERPRETATION OF A SYSTEM OF QUASI-LINEAR ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS UNDER NEUMANN BOUNDARY-CONDITIONS

被引：23

作者：

HU, Y

机构：

[1] Institut de Mathématiques et Informatique, Université Claude Bernard - Lyon I, Villeurbanne

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1993年 / 48卷 / 01期

关键词：

REFLECTING BROWNIAN MOTION; LOCAL TIME; BACKWARD STOCHASTIC DIFFERENTIAL EQUATION; NEUMANN BOUNDARY CONDITION;

D O I：

10.1016/0304-4149(93)90109-H

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：

A probabilistic interpretation of a system of second order quasilinear elliptic partial differential equations under a Neumann boundary condition is obtained by introducing a kind of backward stochastic differential equations in the infinite horizon case. In the same time, a simple proof for the existence and uniqueness result of the classical solution of that Neumann problem is given.

引用

页码：107 / 121

页数：15

共 15 条

[1] [Anonymous], 1975, STOCHASTIC DIFFERENT
[2] DUFFIE D, 1989, STOCHASTIC DIFFERENT
[3] Freidlin M., 1985, FUNCTIONAL INTEGRATI
[4] Friedman A, 1975, STOCHASTIC DIFFERENT, VII
[5] PROBABILISTIC APPROACH TO THE NEUMANN PROBLEM
HSU, P
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (04) : 445 - 472
[6] HSU P, 1984, THESIS STANFORD U ST
[7] HU Y., 1991, STOCH ANAL APPL, V9, P445, DOI [10.1080/07362999108809250, DOI 10.1080/07362999108809250]
[8] Ikeda N., 1981, STOCHASTIC DIFFERENT
[9] ADAPTED SOLUTION OF A BACKWARD STOCHASTIC DIFFERENTIAL-EQUATION
PARDOUX, E
PENG, SG
[J]. SYSTEMS & CONTROL LETTERS, 1990, 14 (01) : 55 - 61
[10] Peng S., 1991, STOCHASTICS, V37, P61

← 1 2 →