Hitting with probability one for stochastic heat equations with additive noise

2023/07/30 by Dalang, Robert C., Pu, Fei
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.16129

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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