Uniform Large Deviations for the Nonlinear Schrödinger Equation with Multiplicative Noise

Eric Gautier

No 2004-42, Working Papers from Center for Research in Economics and Statistics

Abstract: Uniform large deviations for the laws of the paths of the solutionsof the stochastic nonlinear Schr¨odinger equation when the noise converges tozero are presented. The noise is a real multiplicative Gaussian noise. It iswhite in time and colored in space. The path space considered allows blow-upand is endowed with a topology analogue to a projective limit topology. Thusa large variety of large deviation principle may be deduced by contraction. Asa consequence, asymptotics of the tails of the law of the blow-up time whenthe noise converges to zero are obtained.

Date: 2004
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Related works:
Journal Article: Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise (2005)
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