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February 2006 Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H>½
Marco Ferrante, Carles Rovira
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Bernoulli 12(1): 85-100 (February 2006).

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.

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Marco Ferrante. Carles Rovira. "Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H>½." Bernoulli 12 (1) 85 - 100, February 2006.

Information

Published: February 2006
First available in Project Euclid: 28 February 2006

zbMATH: 1102.60054
MathSciNet: MR2202322

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

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Vol.12 • No. 1 • February 2006
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