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March 2010 A stochastic differential game for the inhomogeneous ∞-Laplace equation
Rami Atar, Amarjit Budhiraja
Ann. Probab. 38(2): 498-531 (March 2010). DOI: 10.1214/09-AOP494


Given a bounded $\mathcal{C}^{2}$ domain G⊂ℝm, functions $g\in\mathcal{C}(\partial G,{\mathbb{R}})$ and $h\in\mathcal {C}(\overline{G},{\mathbb{R}}\setminus\{0\})$, let u denote the unique viscosity solution to the equation −2Δu=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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Rami Atar. Amarjit Budhiraja. "A stochastic differential game for the inhomogeneous ∞-Laplace equation." Ann. Probab. 38 (2) 498 - 531, March 2010.


Published: March 2010
First available in Project Euclid: 9 March 2010

zbMATH: 1192.91025
MathSciNet: MR2642884
Digital Object Identifier: 10.1214/09-AOP494

Primary: 35J70 , 49L20 , 91A15 , 91A23

Keywords: Bellman–Isaacs equation , infinity-Laplacian , Stochastic differential games

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 2 • March 2010
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