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Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise

Author

Listed:
  • David Baños

    (University of Oslo)

  • Salvador Ortiz-Latorre

    (University of Oslo)

  • Andrey Pilipenko

    (National Academy of Sciences of Ukraine)

  • Frank Proske

    (University of Oslo)

Abstract

In this paper, we prove the existence of strong solutions to an stochastic differential equation with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters $$H

Suggested Citation

  • David Baños & Salvador Ortiz-Latorre & Andrey Pilipenko & Frank Proske, 2022. "Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise," Journal of Theoretical Probability, Springer, vol. 35(2), pages 714-771, June.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:2:d:10.1007_s10959-021-01084-7
    DOI: 10.1007/s10959-021-01084-7
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    References listed on IDEAS

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    1. Wenbo V. Li & Ang Wei, 2012. "A Gaussian Inequality for Expected Absolute Products," Journal of Theoretical Probability, Springer, vol. 25(1), pages 92-99, March.
    2. Nualart, David & Ouknine, Youssef, 2002. "Regularization of differential equations by fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 103-116, November.
    3. Aida, Shigeki, 2015. "Reflected rough differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3570-3595.
    4. 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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    Cited by:

    1. Iksanov, Alexander & Pilipenko, Andrey, 2023. "On a skew stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 44-68.
    2. Coffie, Emmanuel & Duedahl, Sindre & Proske, Frank, 2023. "Sensitivity analysis with respect to a stochastic stock price model with rough volatility via a Bismut–Elworthy–Li formula for singular SDEs," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 156-195.

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