Catellier, Rémi; Harang, Fabian A. Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation. (English) Zbl 07788715 Ann. Inst. Henri Poincaré, Probab. Stat. 59, No. 3, 1572-1609 (2023). Summary: Existence and uniqueness of solutions to the stochastic heat equation with multiplicative spatial noise is studied. In the spirit of pathwise regularization by noise, we show that a perturbation by a sufficiently irregular continuous path establish wellposedness of such equations, even when the drift and diffusion coefficients are given as generalized functions or distributions. In addition we prove regularity of the averaged field associated to a Lévy fractional stable motion, and use this as an example of a perturbation regularizing the multiplicative stochastic heat equation. Cited in 1 Document MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60H50 Regularization by noise 60L20 Rough paths Keywords:fractional Lévy processes; generalized parabolic Anderson model; pathwise regularization by noise; stochastic heat equation × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] S. Athreya, O. Butkovsky, K. Lê and L. Mytnik. Well-posedness of stochastic heat equation with distributional drift and skew stochastic heat equation, 2020. Available at arXiv:2011.13498 [math]. [2] H. Bahouri, J.-Y. Chemin and R. Danchin. Fourier Analysis and Nonlinear Partial Differential Equations. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 343. Springer, Heidelberg, 2011. Digital Object Identifier: 10.1007/978-3-642-16830-7 Google Scholar: Lookup Link MathSciNet: MR2768550 · Zbl 1227.35004 · doi:10.1007/978-3-642-16830-7 [3] H. Bahouri, J.-Y. Chemin and R. Danchin. 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