SDES WITH OBLIQUE REFLECTION ON NONSMOOTH DOMAINS

被引:105
作者
DUPUIS, P
ISHII, H
机构
[1] UNIV MASSACHUSETTS,AMHERST,MA 01003
[2] CHUO UNIV,DEPT MATH,BUNKYO KU,TOKYO 112,JAPAN
关键词
REFLECTED DIFFUSIONS; STOCHASTIC DIFFERENTIAL EQUATIONS WITH REFLECTION; SKOROKHOD PROBLEM; NONSMOOTH DOMAINS;
D O I
10.1214/aop/1176989415
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
In this paper we consider stochastic differential equations with reflecting boundary conditions for domains that might have corners and for which the allowed directions of reflection at a point on the boundary of the domain are possibly oblique. The main results are strong existence and uniqueness for solutions of such equations. A key ingredient is a family of relatively regular functions appropriate to the given domain and directions of reflection. Two cases are treated in the paper. In the first case the direction of reflection is single valued and varies smoothly, and the main new feature is that the boundary of the domain may be nonsmooth. In the second case the domain is taken to be the intersection of a finite number of domains with relatively smooth boundary, and at the resulting corner points more than one oblique direction is allowed.
引用
收藏
页码:554 / 580
页数:27
相关论文
共 8 条
[1]  
COSTANTINI C, 1987, THESIS U WISCONSIN M
[2]   SOME PROPERTIES OF VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].
CRANDALL, MG ;
EVANS, LC ;
LIONS, PL .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 282 (02) :487-502
[3]   ON OBLIQUE DERIVATIVE PROBLEMS FOR FULLY NONLINEAR 2ND-ORDER ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS ON NONSMOOTH DOMAINS [J].
DUPUIS, P ;
ISHII, H .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (12) :1123-1138
[4]  
Dupuis P., 1991, HOKKAIDO MATH J, V20, P135, DOI [10.14492/hokmj/1381413798, DOI 10.14492/HOKMJ/1381413798]
[5]  
DUPUIS P, 1991, STOCHASTICS, V35, P31
[6]   REFLECTED BROWNIAN-MOTION ON AN ORTHANT [J].
HARRISON, JM ;
REIMAN, MI .
ANNALS OF PROBABILITY, 1981, 9 (02) :302-308
[7]  
Karatzas I., 1988, BROWNIAN MOTION STOC, DOI 10.1007/978-1-4612-0949-2
[8]   STOCHASTIC DIFFERENTIAL-EQUATIONS WITH REFLECTING BOUNDARY-CONDITIONS [J].
LIONS, PL ;
SZNITMAN, AS .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (04) :511-537