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Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise. Well-Posedness, Large Deviations and Support
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 …