Uniform large deviations for the nonlinear Schrödinger equation with multiplicative noise

Eric Gautier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Uniform large deviations for the laws of the paths of the solutions of the stochastic nonlinear Schrödinger 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.

Mots clés: Large deviations; stochastic partial differential equations; nonlinear Schrödinger equation

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Eric Gautier. Uniform large deviations for the nonlinear Schrödinger equation with multiplicative noise. Stochastic Processes and their Applications, 2005, 115 (12), pp.1904-1927. ⟨10.1016/j.spa.2005.06.011⟩. ⟨hal-00003598⟩