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arXiv · 2307.16129

Hitting with probability one for stochastic heat equations with additive noise

Robert C. Dalang·Fei Pu
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Abstract

We study the hitting probabilities of the solution to a system of $d$ stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive $d-6$-dimensional capacity, the solution visits this set almost surely.

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Robert C. Dalang, Fei Pu. 2023-07-30. Hitting with probability one for stochastic heat equations with additive noise. https://arxiv.org/abs/2307.16129

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