Time-Dependent Neutral Stochastic Delay Partial Differential Equations Driven by Rosenblatt Process in Hilbert Space

Abstract

In this paper, we investigate a class of time-dependent neutral stochastic functional differential equations with finite delay driven by Rosenblatt process in a real separable Hilbert space. We prove the existence of unique mild solution by the well-known Banach fixed point principle. At the end we provide a practical example in order to illustrate the viability of our result.

Existence results for second-order neutral stochastic equations driven by Rosenblatt process

“…The Rosenblatt processes can also be inputs in models where self-similarity is observed in empirical data which appears to be non-Gaussian. There exists a consistent literature that focuses on different theoretical aspects of the Rosenblatt processes ( [10,8,12,15]). Some special kind of dynamical systems require mixed process to model its dynamic ( [1,17]).…”