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arXiv · 2108.00881

Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation

Mohammud Foondun·Mathew Joseph·Kunwoo Kim
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Abstract

We consider the stochastic heat equation on $[0,\,1]$ with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball probabilities for the Hölder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these Hölder semi-norms.

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Mohammud Foondun, Mathew Joseph, Kunwoo Kim. 2022-06-01. Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation. https://arxiv.org/abs/2108.00881

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