@article{Sun2024, 
author = {Hui Sun and Yangyang Lyu},
title = {Temporal Hölder continuity of the parabolic Anderson model driven by a class of time-independent Gaussian fields with rough initial conditions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {34838-34862},
keywords = {parabolic Anderson model, Feynman-Kac formula, generalized Gaussian field, Brownian bridge, Hölder continuity, measure-valued initial data},
url = {https://www.sciopen.com/article/10.3934/math.20241659},
doi = {10.3934/math.20241659},
abstract = {In this paper, we considered the parabolic Anderson model with a class of time-independent generalized Gaussian fields on  Rd, 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  u0≡C and  u0∈Cκ(Rd) with  κ∈(0,1].}
}