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

@article{Foondun2022SmallBP, title={Small ball probability estimates for the H{\"o}lder semi-norm of the stochastic heat equation}, author={Mohammud Foondun and Mathew Joseph and Kunwoo Kim}, journal={Probability Theory and Related Fields}, year={2022} }

We consider the stochastic heat equation on $$[0,\,1]$$
[
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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