Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays

Abstract Hermite processes are self-similar processes with stationary increments, the Hermite process of order 1 is fractional Brownian motion and the Hermite process of order 2 is the Rosenblatt process. In this paper we consider a class of time-dependent neutral stochastic functional differential...

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Autor principal:	Hassan,Lakhel El
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2019
Materias:	Neutral stochastic evolution equations Evolution operator Rosenblatt process Wiener integral Banach fixed point theorem.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000400665
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spelling	oai:scielo:S0716-091720190004006652019-11-04Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delaysHassan,Lakhel El Neutral stochastic evolution equations Evolution operator Rosenblatt process Wiener integral Banach fixed point theorem. Abstract Hermite processes are self-similar processes with stationary increments, the Hermite process of order 1 is fractional Brownian motion and the Hermite process of order 2 is the Rosenblatt process. In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by Rosenblatt process with index H ∈ (1/2, 1) which is a special case of a self-similar process with long-range dependence. More precisely, we prove the existence and uniqueness of mild solutions by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is provided to demonstrate the effectiveness of the theoretical result.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.4 20192019-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000400665en10.22199/issn.0717-6279-2019-04-0043
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Neutral stochastic evolution equations Evolution operator Rosenblatt process Wiener integral Banach fixed point theorem.
spellingShingle	Neutral stochastic evolution equations Evolution operator Rosenblatt process Wiener integral Banach fixed point theorem. Hassan,Lakhel El Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays
description	Abstract Hermite processes are self-similar processes with stationary increments, the Hermite process of order 1 is fractional Brownian motion and the Hermite process of order 2 is the Rosenblatt process. In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by Rosenblatt process with index H ∈ (1/2, 1) which is a special case of a self-similar process with long-range dependence. More precisely, we prove the existence and uniqueness of mild solutions by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is provided to demonstrate the effectiveness of the theoretical result.
author	Hassan,Lakhel El
author_facet	Hassan,Lakhel El
author_sort	Hassan,Lakhel El
title	Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays
title_short	Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays
title_full	Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays
title_fullStr	Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays
title_full_unstemmed	Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays
title_sort	neutral stochastic functional differential evolution equations driven by rosenblatt process with varying-time delays
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000400665
work_keys_str_mv	AT hassanlakhelel neutralstochasticfunctionaldifferentialevolutionequationsdrivenbyrosenblattprocesswithvaryingtimedelays
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Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays

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