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May 2008 Exit from a basin of attraction for stochastic weakly damped nonlinear Schrödinger equations
Eric Gautier
Ann. Probab. 36(3): 896-930 (May 2008). DOI: 10.1214/07-AOP344

Abstract

We consider weakly damped nonlinear Schrödinger equations perturbed by a noise of small amplitude. The small noise is either complex and of additive type or real and of multiplicative type. It is white in time and colored in space. Zero is an asymptotically stable equilibrium point of the deterministic equations. We study the exit from a neighborhood of zero, invariant under the flow of the deterministic equation, in L2 or in H1. Due to noise, large fluctuations from zero occur. Thus, on a sufficiently large time scale, exit from these domains of attraction occur. A formal characterization of the small noise asymptotic of both the first exit times and the exit points is given.

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Eric Gautier. "Exit from a basin of attraction for stochastic weakly damped nonlinear Schrödinger equations." Ann. Probab. 36 (3) 896 - 930, May 2008. https://doi.org/10.1214/07-AOP344

Information

Published: May 2008
First available in Project Euclid: 9 April 2008

zbMATH: 1204.60056
MathSciNet: MR2408578
Digital Object Identifier: 10.1214/07-AOP344

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

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 3 • May 2008
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