On Long Time Behavior for Stochastic Nonlinear Schrödinger Equations with a Multiplicative Noise

Abstract In this article, we study mass-critical stochastic nonlinear Schrödinger equations with a multiplicative noise in 3D with a slight time decay ($\langle t \rangle ^{-\epsilon }$ for $\epsilon>0$ arbitrarily small). We prove associated global space-time bounds and the scattering behavior.