Points of slow growth for parabolic SPDEs
Probability
2025-12-18 v1
Abstract
Consider the stochastic PDE, on , subject to , where denotes space-time white noise on and is Lipschitz continuous. It is known that has approximately a Gaussian distribution for every when . Here we prove that there exist random points where the fluctuations of the solution near times zero are almost surely of sharp order . Our work bears some loose resemblance to the study of the slow points of Brownian motion increments, though significant challenges arise due to the infinite-dimensional nature of the present problem.
Cite
@article{arxiv.2512.15177,
title = {Points of slow growth for parabolic SPDEs},
author = {Davar Khoshnevisan and Cheuk Yin Lee},
journal= {arXiv preprint arXiv:2512.15177},
year = {2025}
}