Gautier, Eric (2007) Stochastic nonlinear Schrödinger equations driven by a fractional noise - Well posedness, large deviations and support. Electronic Journal of Probability, 12. pp. 848-861.

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Abstract

We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H∈(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.