A STOCHASTIC DIFFERENTIAL GAME FOR THE INHOMOGENEOUS ∞-LAPLACE EQUATION

• 成果类型: Article
• 署名作者: Atar, Rami; Budhiraja, Amarjit
• 署名单位: Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP494
• 发表日期: 2010
• 页码: 498-531
• 关键词: Existence; CURVATURE

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.