Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension

Florian Bechtold

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arXiv · 2205.04789

Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension

Florian Bechtold

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Abstract

We study a regularization by noise phenomenon for the continuous parabolic Anderson model with a potential shifted along paths of fractional Brownian motion. We demonstrate that provided the Hurst parameter is chosen sufficiently small, this shift allows to establish well-posedness and stability to the corresponding problem - without the need of renormalization - in any dimension. We moreover provide a robustified Feynman-Kac type formula for the unique solution to the regularized problem building upon regularity estimates for the local time of fractional Brownian motion as well as non-linear Young integration.

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Florian Bechtold. 2022-05-10. Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension. https://arxiv.org/abs/2205.04789

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