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Mixed Stochastic Differential Equations: Existence and Uniqueness Result

Author

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  • José Luís Silva

    (University of Madeira)

  • Mohamed Erraoui

    (Université Cadi Ayyad)

  • El Hassan Essaky

    (Université Cadi Ayyad)

Abstract

In this paper we establish an existence and uniqueness result for solutions of multidimensional, time-dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter $$H>1/2$$ H > 1 / 2 and a multidimensional standard Brownian motion under a weaker condition than the Lipschitz one.

Suggested Citation

  • José Luís Silva & Mohamed Erraoui & El Hassan Essaky, 2018. "Mixed Stochastic Differential Equations: Existence and Uniqueness Result," Journal of Theoretical Probability, Springer, vol. 31(2), pages 1119-1141, June.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:2:d:10.1007_s10959-016-0738-9
    DOI: 10.1007/s10959-016-0738-9
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    References listed on IDEAS

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    1. Kubilius, K., 2002. "The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 289-315, April.
    2. Mao, Xuerong, 1995. "Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 281-292, August.
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    Cited by:

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    2. Solesne Bourguin & Thanh Dang & Konstantinos Spiliopoulos, 2023. "Moderate Deviation Principle for Multiscale Systems Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-57, March.

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