A stochastic differential game for the inhomogeneous $\infty$-Laplace equation

Details A stochastic differential game for the inhomogeneous $\infty$-Laplace equation A stochastic differential game for the inhomogeneous $\infty$-Laplace equation

2008-08-11

arxiv.org/abs/0808.1457v2

Annals of Probability 2010, Vol. 38, No. 2, 498-531

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AOP494 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/09-AOP494

Given a bounded $\mathcaligr{C}^2$ domain $G\subset{\mathbb{R}}^m$, functions $g\in\mathcaligr{C}(\partial G,{\mathbb{R}})$ and $h\in\mathcaligr {C}(\bar{G},{\mathbb{R}}\setminus\{0\})$, let $u$ denote the unique viscosity solution to the equation $-2\Delta_{\infty}u=h$ in $G$ with boundary data $g$. We provide a representation for $u$ as the value of a two-player zero-sum stochastic differential game.

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