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

Michael Salins and Samy Tindel

Stochastic Processes and their Applications, 2024, vol. 168, issue C

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.

Keywords: SPDE; Heat equation; Malliavin Calculus; Density; Half-Lipschitz (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104263

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