Weak uniqueness by noise for singular stochastic PDEs

Bertacco, Federico; Orrieri, Carlo; Scarpa, Luca

doi:10.1090/tran/9448

Weak uniqueness by noise for singular stochastic PDEs
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by Federico Bertacco, Carlo Orrieri and Luca Scarpa;

Trans. Amer. Math. Soc.

DOI: https://doi.org/10.1090/tran/9448

Published electronically: April 25, 2025

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Abstract:

We prove weak uniqueness of mild solutions for general classes of SPDEs on a Hilbert space. The main novelty is that the drift is only defined on a Sobolev-type subspace and no Hölder-continuity assumptions are required. This framework turns out to be effective to achieve novel uniqueness results for several specific examples. Such wide range of applications is obtained by exploiting either coloured or rougher-than-cylindrical noises.

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Weak uniqueness by noise for singular stochastic PDEs
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Abstract: