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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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


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:


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.

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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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