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Weak solutions for singular multiplicative SDEs via regularization by noise

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  • Bechtold, Florian
  • Hofmanová, Martina

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.

Suggested Citation

  • Bechtold, Florian & Hofmanová, Martina, 2023. "Weak solutions for singular multiplicative SDEs via regularization by noise," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 413-435.
    • Handle: RePEc:eee:spapps:v:157:y:2023:i:c:p:413-435
    DOI: 10.1016/j.spa.2022.12.010
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    References listed on IDEAS

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    1. Catellier, R. & Gubinelli, M., 2016. "Averaging along irregular curves and regularisation of ODEs," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2323-2366.
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