Joint H\"older continuity of parabolic Anderson model

TL;DR

This paper proves that the solution to the parabolic Anderson model is jointly H"older continuous in both space and time, providing insights into its regularity properties.

Contribution

The paper establishes the joint H"older continuity of the parabolic Anderson model's solution, a novel regularity result for this stochastic PDE.

Findings

Solution is jointly H"older continuous in space and time.

Provides a rigorous mathematical proof of regularity properties.

Enhances understanding of the solution's behavior in stochastic PDEs.

Abstract

We show that the random field solution to the parabolic Anderson equation $(\partial_t-\frac12 \Delta)u=u\diamond \dot{W}$ is jointly H\"older continuous in space and time.