# 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 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.### References

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*Proyecciones (Antofagasta, On line)*, vol. 38, no. 4, pp. 665-689, Oct. 2019.

Copyright (c) 2019 Lakhel El Hassan

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