A STOCHASTIC DIFFERENTIAL GAME FOR THE INHOMOGENEOUS ∞-LAPLACE EQUATION

被引：15

作者：

Atar, Rami ^{[1
]}

Budhiraja, Amarjit ^{[2
]}

机构：

[1] Technion Israel Inst Technol, Dept Elect Engn, IL-32000 Haifa, Israel

[2] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27599 USA

来源：

ANNALS OF PROBABILITY | 2010年 / 38卷 / 02期

关键词：

Stochastic differential games; infinity-Laplacian; Bellman-Isaacs equation; EXISTENCE; CURVATURE;

D O I：

10.1214/09-AOP494

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：

Given a bounded C(2) domain G subset of R(m), functions g is an element of C(partial derivative G, R) and h is an element of C((G) over bar, R backslash {0}), let u denote the unique viscosity solution to the equation -2 Delta(infinity)u = h in G with boundary data g. We provide a representation for u as the value of a two-player zero-sum stochastic differential game.

引用

页码：498 / 531

页数：34