Long time behavior of fractional impulsive stochastic differential equations with infinite delay

This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive stochastic differential equations with infinite delay driven by both K-valued Q-cylindrical Brownian motion and fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). A general...

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Detalles Bibliográficos
Autores: Xu, Jiaohui, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/88952
Acceso en línea:https://hdl.handle.net/11441/88952
https://doi.org/10.3934/dcdsb.2018272
Access Level:acceso abierto
Palabra clave:Impulsive differential equations
Fractional derivative
Fractional Brownian motion
Infinite delay
Exponential asymptotic behaviour
Descripción
Sumario:This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive stochastic differential equations with infinite delay driven by both K-valued Q-cylindrical Brownian motion and fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). A general framework which provides an effective way to prove the continuous dependence of mild solutions on initial value is established under some appropriate assumptions. Furthermore, it is also proved the exponential decay to zero of solutions to fractional stochastic impulsive differential equations with infinite delay.