Uniform large deviations for the nonlinear Schrödinger equation with multiplicative noise

2004/12/16 by Éric Gautier, Eric Gautier · 1 citation
Economics, Econometrics and Finance · Mathematics · #Mathematical Biology Tumor Growth #Stochastic processes and financial applications #advanced mathematical theories #math.AP #math.PR #msc:35Q55 #msc:60F10 #msc:60H15

paper · pdf · doi:10.1016/j.spa.2005.06.011

published as Stochastic Process. Appl. 115, Issue 12, December 2005, pp. 1904-1927

arxiv created 2004/12/16 · openalex publication_date 2005/08/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

Uniform large deviations for the laws of the paths of the solutions of the stochastic nonlinear Schrodinger equation when the noise converges to zero are presented. The noise is a real multiplicative Gaussian noise. It is white in time and colored in space. The path space considered allows blow-up and is endowed with a topology analogue to a projective limit topology. Thus a large variety of large deviation principle may be deduced by contraction. As a consequence, asymptotics of the tails of the law of the blow-up time when the noise converges to zero are obtained.

Citations

• Solitary Wave Dynamics in an External Potential
• Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise
• Large deviations and support results for nonlinear Schrödinger equations with additive noise and applications

Cited by

• Large Deviations for Nonlinear Stochastic Schrodinger Equation