Small-ball constants, and exceptional flat points of SPDEs
Probability
2023-12-12 v1
Abstract
We study small-ball probabilities for the stochastic heat equation with multiplicative noise in the moderate-deviations regime. We prove the existence of a small-ball constant and related it to other known quantities in the literature. These small-ball estimates are known to imply Chung-type laws of the iterated logarithm (LIL) at typical spatial points; these points can be thought of as "points of flat growth". For this result in a similar context in SPDEs see, for example, the recent work of Chen \cite{Ch2023}. We establish the existence of a new family of exceptional spatial points where the Chung-type LIL fails.
Keywords
Cite
@article{arxiv.2312.05789,
title = {Small-ball constants, and exceptional flat points of SPDEs},
author = {Davar Khoshnevisan and Kunwoo Kim and Carl Mueller},
journal= {arXiv preprint arXiv:2312.05789},
year = {2023}
}
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37 pages