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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 29 open journal systems 


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

Eric Gautier, Yale University and CREST


Abstract
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.


Full text: PDF

Pages: 848-861

Published on: June 4, 2007
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Electronic Journal of Probability. ISSN: 1083-6489