Weak solutions for singular multiplicative SDEs via regularization by noise

We study multiplicative SDEs perturbed by an independent additive fractional Brownian motion. Provided the Hurst parameter is chosen in a specified regime, we establish existence of probabilistically weak solutions to the SDE if the measurable diffusion coefficient merely satisfies an integrability condition. In particular, this allows to consider certain singular diffusion coefficients. (c) 2022 Published by Elsevier B.V.