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Convergence of delay differential equations driven by fractional Brownian motion

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Abstract

In this note, we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L p, to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed App., Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Marco Ferrante

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Carles Rovira

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  1. Marco Ferrante
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  2. Carles Rovira
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Correspondence to Carles Rovira.

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Ferrante, M., Rovira, C. Convergence of delay differential equations driven by fractional Brownian motion. J. Evol. Equ. 10, 761–783 (2010). https://doi.org/10.1007/s00028-010-0069-8

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  • DOI: https://doi.org/10.1007/s00028-010-0069-8

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