Stochastic nonlinear Schrodinger equations driven by a fractional noise - Well posedness, large deviations and support
Probability
2007-11-08 v1 Analysis of PDEs
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). 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.
Keywords
Cite
@article{arxiv.math/0609423,
title = {Stochastic nonlinear Schrodinger equations driven by a fractional noise - Well posedness, large deviations and support},
author = {Eric Gautier},
journal= {arXiv preprint arXiv:math/0609423},
year = {2007}
}