On Besov regularity and local time of the solution to the stochastic heat equation

Abstract

Sharp Besov regularities in time and space variables are investigated for (u(t, x), t ∈ [0, T ], x ∈ R), 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.