On Besov regularity and local time of the stochastic heat equation

Brahim Boufoussi; Yassine Nachit

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arXiv · 2006.04235

On Besov regularity and local time of the stochastic heat equation

Brahim Boufoussi·Yassine Nachit

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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, H\"{o}lder 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.

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Brahim Boufoussi, Yassine Nachit. 2020-06-07. On Besov regularity and local time of the stochastic heat equation. https://arxiv.org/abs/2006.04235

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