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Stochastic heat equation with distributional drift

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If you have a question about this talk, please contact Yuzhao Wang.

We study stochastic reaction–diffusion equation with a distributional drift. We obtain existence and uniqueness of a strong solution whenever the drift belongs to a suitable Besov space. This class includes equations with drift being measures, in particular, Dirac delta masses which corresponds to the skewed stochastic heat equation. Our results extend the work of Bass and Chen (2001) to the framework of stochastic partial differential equations and generalize the results of Gyöngy and Pardoux (1993) to distributional drifts. To establish these results, we exploit the regularization effect of the white noise through a new strategy based on the stochastic sewing lemma introduced in Lê (2020). This talk is based on the joint work with Siva Athreya, Oleg Butkovsky and Leonid Mytnik, arXiv:2011.13498.

This talk is part of the Analysis seminar series.

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