Abstract: As an important self-similar stochastic process, Rosenblatt process is often used to describe non-Gaussian random phenomena. In order to further characterize stochastic phenomena driven by Rosenblatt process, we study the mild solution for a class of time-dependent stochastic evolution equations with finite delay driven by Rosenblatt process in this paper. An existence and uniqueness theorem for the mild solution to this class of stochastic evolution equations is obtained by means of the Banach fixed point theorem in a real separable Hilbert space with time-dependent, and an example is proposed to illustrate the result.

Key words: stochastic evolution equation, evolution operator, Rosenblatt process, fixed point theorem, mild solution