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.
|Place of Publication||Ithaca, New York|
|Number of pages||47|
|Publication status||Published - 2 Aug 2021|
- heat equation
- white noise
- stochastic partial differential equations
- small ball