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

Authors

Mohammud Foondun, University of Strathclyde
Mathew Joseph, Indian Statistical Institute Bangalore
Kunwoo Kim, Pohang University of Science and Technology

Article Type

Research Article

Publication Title

Probability Theory and Related Fields

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.

First Page

553

Last Page

613

DOI

https://10.1007/s00440-022-01153-w

Publication Date

2-1-2023

Comments

Open Access, Hybrid Gold

Recommended Citation

Foondun, Mohammud; Joseph, Mathew; and Kim, Kunwoo, "Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation" (2023). Journal Articles. 3872.
https://digitalcommons.isical.ac.in/journal-articles/3872