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Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term

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  • Salins, Michael
  • Tindel, Samy

Abstract

We prove the existence of a density for the solution to the multiplicative semilinear stochastic heat equation on an unbounded spatial domain, with drift term satisfying a half-Lipschitz type condition. The methodology is based on a careful analysis of differentiability for a map defined on weighted functional spaces.

Suggested Citation

  • Salins, Michael & Tindel, Samy, 2024. "Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:spapps:v:168:y:2024:i:c:s0304414923002351
    DOI: 10.1016/j.spa.2023.104263
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    References listed on IDEAS

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    1. Márquez-Carreras, D. & Mellouk, M. & Sarrà, M., 2001. "On stochastic partial differential equations with spatially correlated noise: smoothness of the law," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 269-284, June.
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