The Annals of Probability

A stochastic differential game for the inhomogeneous ∞-Laplace equation

Rami Atar and Amarjit Budhiraja

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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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Ann. Probab., Volume 38, Number 2 (2010), 498-531.

First available in Project Euclid: 9 March 2010

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Zentralblatt MATH identifier

Primary: 91A15: Stochastic games 91A23: Differential games [See also 49N70] 35J70: Degenerate elliptic equations 49L20: Dynamic programming method

Stochastic differential games infinity-Laplacian Bellman–Isaacs equation


Atar, Rami; Budhiraja, Amarjit. A stochastic differential game for the inhomogeneous ∞-Laplace equation. Ann. Probab. 38 (2010), no. 2, 498--531. doi:10.1214/09-AOP494.

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