Stochastic nonlinear Schrodinger equations driven by a fractional noise - Well posedness, large deviations and support

Details Stochastic nonlinear Schrodinger equations driven by a fractional noise - Well posedness, large deviations and support Stochastic nonlinear Schrodinger equations driven by a fractional noise - Well posedness, large deviations and support

2006-09-14

arxiv.org/abs/math/0609423v1

Electronic Journal of Probability 12, June 2007, pp. 848-861

Mathematics

Probability

Scientific paper

We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0,1). It is also colored in space and the space correlation operator is assumed to be nuclear. We study the local well-posedness of the equation. Under adequate assumptions on the initial data, the space correlations of the noise and for some saturated nonlinearities, we prove a sample path large deviations principle and a support result. These results are stated in a space of exploding paths which are Holder continuous in time until blow-up. We treat the case of Kerr nonlinearities when H > 1/2.

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