Regularization by noise for stochastic Hamilton-Jacobi equations

Published 22 Sep 2016 in math.PR and math.AP | (1609.07074v2)

Abstract: We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path $L^{\infty}$ bounds for the second derivative of solutions to such PDE are shown. These bounds are expressed as solutions to reflected SDE and are shown to be optimal.

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