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Convergence of delay differential equations driven by fractional Brownian motion. (English) Zbl 1239.60040
Summary: 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.

60H05Stochastic integrals
60H07Stochastic calculus of variations and the Malliavin calculus
60H10Stochastic ordinary differential equations
60G22Fractional processes, including fractional Brownian motion
Full Text: DOI arXiv
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