Existence and exponential stability for neutral stochastic integro–differential equations with impulses driven by a Rosenblatt process

Tomás Caraballo; Carlos Ogouyandjou; Fulbert Kuessi Allognissode; Mamadou Abdoul Diop

doi:10.3934/dcdsb.2019251

Article Contents

2020, Volume 25, Issue 2: 507-528. Doi: 10.3934/dcdsb.2019251

This issue Previous Article Multiplicity results for fourth order problems related to the theory of deformations beams Next Article A Favard type theorem for Hurwitz polynomials

Existence and exponential stability for neutral stochastic integro–differential equations with impulses driven by a Rosenblatt process

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012-Sevilla, Spain
2.
Université d'Abomey-Calavi(UAC), Institut de Mathématiques et de Sciences Physiques(IMSP), 01 B.P. 613, Porto-Novo, République du Bénin
3.
Université Gaston Berger de Saint-Louis, UFR SAT Département de Mathématiques, B.P234, Saint-Louis, Sénégal

Received: December 31, 2018

Revised: February 28, 2019

Early access: November 2019

Published: February 2020

This work has been partially supported by FEDER and the Spanish Ministerio de Economía y Competitividad project MTM2015-63723-P and the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) under Proyecto de Excelencia P12-FQM-1492

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Abstract

The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed in this work by using the Banach fixed point theorem and the theory of resolvent operator developed by R. Grimmer in [12]. Furthermore, the exponential stability in mean square for the mild solution to neutral stochastic integro–differential equations with Rosenblatt process is obtained by establishing an integral inequality. Finally, an example is exhibited to illustrate the abstract theory.

Keywords:

Exponential stability,
resolvent operator,
impulsive neutral stochastic integro–differential equations,
Rosenblatt process.

Mathematics Subject Classification: 60H15, 35R60.

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