Bernoulli

  • Bernoulli
  • Volume 12, Number 1 (2006), 85-100.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H>½

Marco Ferrante and Carles Rovira

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Abstract

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>½. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Article information

Source
Bernoulli, Volume 12, Number 1 (2006), 85-100.

Dates
First available in Project Euclid: 28 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1141136650

Mathematical Reviews number (MathSciNet)
MR2202322

Zentralblatt MATH identifier
1102.60054

Keywords
fractional Brownian motion stochastic delay differential equation

Citation

Ferrante, Marco; Rovira, Carles. Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H>½. Bernoulli 12 (2006), no. 1, 85--100. https://projecteuclid.org/euclid.bj/1141136650


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