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

Foondun, Mohammud and Joseph, Mathew and Kim, Kunwoo (2022) Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation. Probability Theory and Related Fields. ISSN 0178-8051 (https://doi.org/10.1007/s00440-022-01153-w)

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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.