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2006

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/23389

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

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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>¿. 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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Equacions diferencials estocàstiques, Moviment brownià

Subject (English)

Stochastic differential equations, Brownian movements

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FERRANTE, Marco and ROVIRA ESCOFET, Carles. Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2. Bernoulli. 2006. Vol. 12, num. 1, pags. 85-100. ISSN 1350-7265. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/23389

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