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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.4 Antofagasta dic. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-04-0043 

Articles

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

1 Cadi Ayyad University, National School of Applied Sciences, Safi, Morocco e-mail: e.lakhel@uca.ma

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.

Keywords: Neutral stochastic evolution equations; Evolution operator; Rosenblatt process; Wiener integral; Banach fixed point theorem.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgements

The author would like to thank the referee and the editor for their careful comments and valuable suggestions on this work.

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Received: April 2018; Accepted: July 2019

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