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

peer reviewedSharp Besov regularities in time and space variables are investigated for (Formula presented.), 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 (Formula presented.) viewed either as a process in the space variable or time variable. Hausdorff dimensions of their corresponding level sets are also obtained