Temporal Hölder continuity of the parabolic Anderson model driven by a class of time-independent Gaussian fields with rough initial conditions - Hui Sun; Yangyang Lyu (AIMS Mathematics)
In this paper, we considered the parabolic Anderson model with a class of time-independent generalized Gaussian fields on $ \mathbb{R}^d $, which included fractional white noise, Bessel field, massive free field, and other nonstationary Gaussian fields. Under the rough initial conditions, we constructed the Feynman-Kac formula as a solution in the Stratonovich integral by Brownian bridge, and then proved the Hölder continuity of the solution with respect to the time variable. As a comparison, we also studied the Hölder continuity under the regular initial conditions that $ u_0\equiv C $ and $ u_0\in C^κ(\mathbb{R}^d) $ with $ κ\in(0, 1] $.