On Besov regularity and local time of the stochastic heat equation

Abstract

Sharp Besov regularities in time and space variables are investigated for $\left(u(t,x),t\in [0,T],x\in \mathbb{R}\right)$, the mild solution to the stochastic heat equation driven by space-time white noise. Existence, Hölder continuity, and Besov regularity of local times are established for $u(t,x)$ viewed either as a process in the space variable or time variable. Hausdorff dimensions of their corresponding level sets are also obtained.

References in corpus (2)

• The Stochastic Heat Equation with a Fractional-Colored Noise: Existence of the Solution
• Joint continuity of the local times of fractional Brownian sheets