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...

ver descrição completa

Detalhes bibliográficos
Autores: Ferrante, Marco, Rovira Escofet, Carles
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/23389
Acesso em linha:https://hdl.handle.net/2445/23389
Access Level:acceso abierto
Palavra-chave:Equacions diferencials estocàstiques
Moviment brownià
Stochastic differential equations
Brownian movements
Descrição
Resumo: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.