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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Resumen

HASSAN, Lakhel El. Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays. Proyecciones (Antofagasta) [online]. 2019, vol.38, n.4, pp.665-689. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-2019-04-0043.

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.

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

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