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 , 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 viewed either as a process in the space variable or time variable. Hausdorff dimensions of their corresponding level sets are also obtained.