Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise Well Posedness, Large Deviations and Support
We consider stochastic nonlinear Schr¨odinger equations driven byan 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 tobe nuclear. We study the local well-posedness of the equation. Under adequateassumptions on the initial data, the space correlations of the noise and for somesaturated nonlinearities, we prove a sample path large deviations principle and asupport result. These results are stated in a space of exploding paths which areH¨older continuous in time until blow-up. We treat the case of Kerr nonlinearitieswhen H > 12 .
Year of publication: |
2006
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Authors: | Gautier, Eric |
Institutions: | Centre de Recherche en Économie et Statistique (CREST), Groupe des Écoles Nationales d'Économie et Statistique (GENES) |
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