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 spacetime 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.04235
 arXiv:
 arXiv:2006.04235
 Bibcode:
 2020arXiv200604235B
 Keywords:

 Mathematics  Probability;
 Mathematics  Analysis of PDEs;
 60G15;
 60G17;
 60H05;
 60H15