Existence of weak pullback mean random attractors for stochastic Schrödinger lattice systems driven by superlinear noise

Abstract

This paper is concerned with the random dynamics of stochastic Schrödinger lattice systems driven by superlinear noise. We first prove the existence and uniqueness of solutions when the nonlinear noise has a superlinear growth order by defining a globally Lipschitz continuous cut-off function to approximate the locally Lipschitz drift and diffusion terms, and then define a mean random dynamical system associated with the solution operators. At last, we establish the existence and uniqueness of weak pullback mean random attractors in $ L^2(\Omega,\ell^2) $.