Invariant measures and random attractors of stochastic delay differential equations in Hilbert space

This paper is devoted to a general stochastic delay differential equation with infinite-dimensional diffusions in Hilbert space. We not only investigate the existence of invariant measures either Wiener process or Lévy jump process, but also obtain pullback attractor under process. In particular, we prove non-trivial stationary solution which exponentially stable and generated by composition random variable shift. At last, examples reaction-diffusion equations noise are provided illustrate our results.