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2007 Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise. Well-Posedness, Large Deviations and Support
Eric Gautier
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Electron. J. Probab. 12: 848-861 (2007). DOI: 10.1214/EJP.v12-416

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 $H > 1/2$.

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Eric Gautier. "Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise. Well-Posedness, Large Deviations and Support." Electron. J. Probab. 12 848 - 861, 2007. https://doi.org/10.1214/EJP.v12-416

Information

Accepted: 4 June 2007; Published: 2007
First available in Project Euclid: 1 June 2016

zbMATH: 1127.60057
MathSciNet: MR2318412
Digital Object Identifier: 10.1214/EJP.v12-416

Subjects:
Primary: 60F10
Secondary: 35Q55, 60H15

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Vol.12 • 2007
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