Scattering for stochastic nonlinear Schrödinger equations
We study the scattering behavior of global solutions to stochastic nonlinear
Schr\"odinger 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.
368
2
843–884
843–884
Springer