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

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 b...

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Detalles Bibliográficos
Autores: Ferrante, Marco, Rovira Escofet, Carles
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/23389
Acceso en línea:https://hdl.handle.net/2445/23389
Access Level:acceso abierto
Palabra clave:Equacions diferencials estocàstiques
Moviment brownià
Stochastic differential equations
Brownian movements
Descripción
Sumario: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.