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Weak solutions for singular multiplicative SDEs via regularization by noise (2203.13745v1)
Published 25 Mar 2022 in math.PR
Abstract: We study multiplicative SDEs perturbed by an additive fractional Brownian motion on another probability space. 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.