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

Eric Gautier

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arXiv · math/0609423

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

Eric Gautier

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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 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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Eric Gautier. 2006-09-14. Stochastic nonlinear Schrodinger equations driven by a fractional noise - Well posedness, large deviations and support. https://arxiv.org/abs/math/0609423

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