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Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

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We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. 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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Bernoulli Society for Mathematical Statistics and Probability

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(c) ISI/BS, International Statistical Institute, Bernoulli Society, 2006

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2