A Stochastic Differential game for the inhomogeneous infinity-Laplace equation

Series: 
Stochastics Seminar
Thursday, September 30, 2010 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 002
,  
University of North Carolina at Chapel Hill
A two-player zero-sum stochastic differential game, defined in terms of an m-dimensional state process that is driven by a one-dimensional Brownian motion, played until the state exits the domain, is studied.The players controls enter in a diffusion coefficient and in an unbounded drift coefficient of the state process. We show that the game has value, and characterize the value function as the unique viscosity solution of an inhomogeneous infinity Laplace equation.Joint work with R. Atar.