“…And then by the compactness method and the Prokhorov theorem, we obtain the existence of invariant measures (see Theorem 4.2). In addition, if f is periodic in t, we further show such an invariant measure is also periodic, which is different from [15,18,29,32] where the periodic measures do not have invariant property. For the existence of invariant measures of autonomous systems, we refer the reader to [13,46] for stochastic lattice systems and [6,14,30,37,52] for stochastic partial differential equations.…”