Regularization by noise for stochastic Hamilton-Jacobi equations

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.

References in corpus (3)

• Noise Prevents Singularities in Linear Transport Equations
• Strong uniqueness for SDEs in Hilbert spaces with nonregular drift
• Singular Equations Driven by an Additive Noise and Applications

Cited by in corpus (3)

• Stochastic nonlinear Fokker-Planck equations
• Well-posedness by noise for scalar conservation laws
• Rescaling nonlinear noise for 1D stochastic parabolic equations