H\"older regularity of Hamilton-Jacobi equations with stochastic forcing

TL;DR

This paper establishes space-time H"older regularity estimates for solutions of stochastic Hamilton-Jacobi equations, showing bounds depend on Hamiltonian growth and stochastic coefficient regularity, invariant under hyperbolic scaling.

Contribution

It provides novel regularity estimates for stochastic Hamilton-Jacobi equations that are invariant under hyperbolic scaling, linking solution regularity to Hamiltonian growth and stochastic coefficient smoothness.

Findings

Solutions exhibit space-time H"older regularity under stochastic forcing.

Regularity bounds depend only on Hamiltonian growth and stochastic coefficient regularity.

Results are invariant under hyperbolic scaling.

Abstract

We obtain space-time H\"older regularity estimates for solutions of first- and second-order Hamilton-Jacobi equations perturbed with an additive stochastic forcing term. The bounds depend only on the growth of the Hamiltonian in the gradient and on the regularity of the stochastic coefficients, in a way that is invariant with respect to a hyperbolic scaling.