Journal of Evolution Equations

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

Convergence of delay differential equations driven by fractional Brownian motion

  • Marco Ferrante
  • Carles RoviraEmail author


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.

Mathematics Subject Classification (2000)

60H05 60H07 


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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