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Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Author

Listed:
  • Robert C. Dalang

    (École Polytechnique Fédérale de Lausanne)

  • Fei Pu

    (Beijing Normal University)

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.

Suggested Citation

  • Robert C. Dalang & Fei Pu, 2024. "Hitting with Probability One for Stochastic Heat Equations with Additive Noise," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3479-3495, November.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:4:d:10.1007_s10959-024-01342-4
    DOI: 10.1007/s10959-024-01342-4
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