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We study a regularization by noise phenomenon for the continuous parabolicAnderson model with a potential shifted along paths of fractional Brownianmotion. We demonstrate that provided the Hurst parameter is chosen sufficientlysmall, this shift allows to establish well-posedness and stability to thecorresponding problem - without the need of renormalization - in any dimension.We moreover provide a robustified Feynman-Kac type formula for the uniquesolution to the regularized problem building upon regularity estimates for thelocal time of fractional Brownian motion as well as non-linear Youngintegration.

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