Scattering for stochastic nonlinear Schrödinger equations

Abstract

We study the scattering behavior of global solutions to stochastic nonlinear Schrödinger equations with linear multiplicative noise. In the case where the quadratic variation of the noise is globally finite and the nonlinearity is defocusing,we prove that the solutions scatter at infinity in the pseudo-conformal space and in the energy space respectively, including the energy-critical case. Moreover, in the case where the noise is large, non-conservative and has infinite quadratic variation, we show that the solutions scatter at infinity with high probability for all energy-subcritical exponents.