Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Robert C. Dalang () and Fei Pu ()
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Robert C. Dalang: École Polytechnique Fédérale de Lausanne
Fei Pu: Beijing Normal University

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3479-3495

Abstract: 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 $$(d-6)$$ ( d - 6 ) -dimensional capacity, the solution visits this set almost surely.

Keywords: Hitting probability; Stochastic heat equations; Capacity; Invariant measure; Primary 60H15; 60J45; Secondary 47D07; 60G60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01342-4

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