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

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 R. Grimmer, Resolvent operators for integral equations in a...

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Autores: Caraballo Garrido, Tomás, Ogouyandjou, Carlos, Allognissode, Fulbert Kuessi, Diop, Mamadou Abdoul
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/100802
Acceso en línea:https://hdl.handle.net/11441/100802
https://doi.org/10.3934/dcdsb.2019251
Access Level:acceso abierto
Palabra clave:Exponential stability
Resolvent operator
Impulsive neutral stochastic integro-differential equations
Rosenblatt process
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spelling Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt processCaraballo Garrido, TomásOgouyandjou, CarlosAllognissode, Fulbert KuessiDiop, Mamadou AbdoulExponential stabilityResolvent operatorImpulsive neutral stochastic integro-differential equationsRosenblatt processThe 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 R. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc., 273 (1982), 333–349. 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.American Institute of Mathematical Sciences (AIMS)Ecuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas DiferencialesEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y Competitividad (MINECO). EspañaJunta de Andalucía. Consejería de Innovación, Ciencia y Empresa2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/100802https://doi.org/10.3934/dcdsb.2019251reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete and Continuous Dynamical Systems - Series B, 25 (2), 507-528.MTM2015-63723-PP12-FQM-1492https://www.aimsciences.org/article/doi/10.3934/dcdsb.2019251info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1008022026-06-17T12:51:07Z
dc.title.none.fl_str_mv Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
title Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
spellingShingle Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
Caraballo Garrido, Tomás
Exponential stability
Resolvent operator
Impulsive neutral stochastic integro-differential equations
Rosenblatt process
title_short Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
title_full Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
title_fullStr Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
title_full_unstemmed Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
title_sort Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Ogouyandjou, Carlos
Allognissode, Fulbert Kuessi
Diop, Mamadou Abdoul
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Ogouyandjou, Carlos
Allognissode, Fulbert Kuessi
Diop, Mamadou Abdoul
author_role author
author2 Ogouyandjou, Carlos
Allognissode, Fulbert Kuessi
Diop, Mamadou Abdoul
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
Ministerio de Economía y Competitividad (MINECO). España
Junta de Andalucía. Consejería de Innovación, Ciencia y Empresa
dc.subject.none.fl_str_mv Exponential stability
Resolvent operator
Impulsive neutral stochastic integro-differential equations
Rosenblatt process
topic Exponential stability
Resolvent operator
Impulsive neutral stochastic integro-differential equations
Rosenblatt process
description 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 R. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Amer. Math. Soc., 273 (1982), 333–349. 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.
publishDate 2020
dc.date.none.fl_str_mv 2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/100802
https://doi.org/10.3934/dcdsb.2019251
url https://hdl.handle.net/11441/100802
https://doi.org/10.3934/dcdsb.2019251
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems - Series B, 25 (2), 507-528.
MTM2015-63723-P
P12-FQM-1492
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2019251
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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