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On near optimal trajectories for a game associated with the -Laplacian

Summary: On near optimal trajectories for a game
associated with the -Laplacian
Rami Atar and Amarjit Budhiraja
December 1, 2008; Last revised May 10, 2010
Abstract: A two-player stochastic differential game representation has recently been ob-
tained for solutions of the equation -u = h in a C2
domain with Dirichlet boundary
condition, where h is continuous and takes values in R \ {0}. Under appropriate assump-
tions, including smoothness of u, we identify a family of diffusion processes that may arise
as the vanishing limit law of the state process, when both players play -optimally. We
also identify the limit law of the state process under a sequence of near saddle points.
AMS 2000 subject classifications: 91A15, 91A23, 35J70
Keywords: Stochastic differential games; Infinity-Laplacian; Bellman-Issacs equations
1. Introduction and main result
Consider the equation

-2u = h in G,
u = g on G,


Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology


Collections: Engineering