Wasserstein convergence rate of invariant measures for stochastic Schrödinger delay lattice systems

Abstract

This paper is concerned with the convergence of invariant measures in the Wasserstein sense for the stochastic Schrödinger delay lattice systems as delay parameter ρ or parameter β approaches zero. Through pth-order moment estimates of solutions to systems, as well as the Hölder continuity estimates of solutions with respect to time, we obtain the convergence of solutions about initial data and the above parameters. Then together with high-order moment estimates of invariant measures, we prove that the unique invariant measure of such delay lattice system converges to the invariant measure of limiting system in the Wasserstein sense as delay parameter ρ or parameter β approaches zero, and the corresponding convergence rate is also obtained.