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

Mohammud Foondun, Mathew Joseph, Kunwoo Kim

Research output: Working paperWorking Paper/Preprint

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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.
Original languageUndefined/Unknown
Place of PublicationIthaca, New York
Number of pages47
Publication statusPublished - 2 Aug 2021

Keywords

  • heat equation
  • white noise
  • stochastic partial differential equations
  • small ball

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