Weak solutions for singular multiplicative SDEs via regularization by noise

Florian Bechtold and Martina Hofmanová

Stochastic Processes and their Applications, 2023, vol. 157, issue C, 413-435

Abstract: 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.

Keywords: Stochastic differential equations, Regularization by noise, Multiplicative noise, Young integration, Rough path theory, Weak solutions (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:157:y:2023:i:c:p:413-435

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DOI: 10.1016/j.spa.2022.12.010

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