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Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise. Well-Posedness, Large Deviations and Support


 
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1. Title Title of document Stochastic Nonlinear Schrödinger Equations Driven by a Fractional Noise. Well-Posedness, Large Deviations and Support
 
2. Creator Author's name, affiliation, country Eric Gautier; Yale University and CREST
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Large deviations; stochastic partial differential equations; nonlinear Schrodinger equation; fractional Brownian motion
 
3. Subject Subject classification 60F10, 60H15, 35Q55
 
4. Description 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 $H > 1/2$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2007-06-04
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/416
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-416
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
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