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A Feynman–Kac formula for stochastic Dirichlet problems

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  • Gerencsér, Máté
  • Gyöngy, István

Abstract

A representation formula for solutions of stochastic partial differential equations with Dirichlet boundary conditions is proved. The scope of our setting is wide enough to cover the general situation when the backward characteristics that appear in the usual formulation are not even defined in the Itô sense.

Suggested Citation

  • Gerencsér, Máté & Gyöngy, István, 2019. "A Feynman–Kac formula for stochastic Dirichlet problems," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 995-1012.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:3:p:995-1012
    DOI: 10.1016/j.spa.2018.04.003
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    References listed on IDEAS

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    1. Kim, Kyeong-Hun, 2004. "On stochastic partial differential equations with variable coefficients in C1 domains," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 261-283, August.
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