We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter $H \in (0,1)$ and colored in space with a nuclear space correlation operator. We study local well-posedness. Under adequate assumptions on the initial data, the space correlations of the noise and for some saturated nonlinearities, we prove sample path large deviations and support results in a space of Holder continuous in time until blow-up paths. We consider Kerr nonlinearities when $H > 1/2$.
"Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise. Well-Posedness, Large Deviations and Support." Electron. J. Probab. 12 848 - 861, 2007. https://doi.org/10.1214/EJP.v12-416