Journal of Evolution Equations

, Volume 10, Issue 4, pp 761–783 | Cite as

Convergence of delay differential equations driven by fractional Brownian motion

Article

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 Lp, to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.

Mathematics Subject Classification (2000)

60H05 60H07 

Keywords

Stochastic differential delay equations Fractional Brownian motion Riemann–Stieltjes integral 

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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica Pura ed App.Università di PadovaPadovaItaly
  2. 2.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

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