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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