Revista de la
Unión Matemática Argentina
Asymptotic mean value formulas for parabolic nonlinear equations
Pablo Blanc, Fernando Charro, Juan J. Manfredi and Julio D. Rossi
Volume 64, no. 1 (2022), pp. 137–164

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In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games.