Stochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motion

Ahmed Boudaoui; Tomás Caraballo; Abdelghani Ouahab

doi:10.3934/dcdsb.2017084

Article Contents

2017, Volume 22, Issue 7: 2521-2541. Doi: 10.3934/dcdsb.2017084

This issue Previous Article Next Article Bifurcation and final patterns of a modified Swift-Hohenberg equation

Stochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motion

1.
Laboratory of Mathematics, Univ Sidi Bel Abbes, PoBox 89,22000 Sidi-Bel-Abbes, Algeria
2.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160,41080 Sevilla, Spain

¹ Corresponding author
¹ Corresponding author

Received: June 30, 2016

Revised: August 31, 2016

Published: October 2017

This work has been partially supported by grant MTM2015-63723-P (MINECO/FEDER, EU) and Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) under grant 2010/FQM314 and Proyecto de Excelencia P12-FQM-1492.

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Abstract

This paper is concerned with the existence and continuous dependence of mild solutions to stochastic differential equations with non-instantaneous impulses driven by fractional Brownian motions. Our approach is based on a Banach fixed point theorem and Krasnoselski-Schaefer type fixed point theorem.

Keywords:

Fractional Brownian motion,
fixed point,
mild solutions,
stochastic functional differential equation.

Mathematics Subject Classification: Primary:34A12, 34A37;Secondary:35A01, 60H15, 60H20.

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