SOLVABILITY OF THE NONLINEAR DIRICHLET PROBLEM WITH INTEGRO-DIFFERENTIAL OPERATORS

被引：3

作者：

Bayraktar, Erhan ^{[1
]}

Song, Qingshuo ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] City Univ Hong Kong, Kowloon, Hong Kong, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2018年 / 56卷 / 01期

基金：

美国国家科学基金会;

关键词：

boundary value problem; Skorokhod topology; integro-differential equation; viscosity solution; Levy process; stochastic exit control problem; STOCHASTIC PERRONS METHOD; VISCOSITY SOLUTIONS; LIFETIME RUIN; EQUATIONS; VERIFICATION; PROBABILITY;

D O I：

10.1137/17M1130241

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper analyzes the solvability of a class of elliptic nonlinear Dirichlet problems with jumps. The contribution of the paper is the construction of the supersolution required in Perron's method. This is achieved by solving the exit time problem of an Ito jump diffusion. The proof of this relies on the proof of continuity of the entrance time and point with respect to the Skorokhod topology.

引用

页码：292 / 315

页数：24

共 25 条

[1] Viscosity solutions of nonlinear integro-differential equations [J].