2004/06/18 by Éric Gautier, Eric Gautier · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #math.AP #math.PR #msc:35Q51 #msc:35Q55 #msc:60F10 #msc:60H15
paper · pdf · doi:10.1051/ps:2005005
published as ESAIM: P&S, April 2005, Vol. 9, pp. 74-97
arxiv created 2004/06/18 · openalex publication_date 2005/04/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
Sample path large deviations for the laws of the solutions of stochastic nonlinear Schrödinger equations when the noise converges to zero are presented. The noise is a complex additive Gaussian noise. It is white in time and colored in space. The solutions may be global or blow-up in finite time, the two cases are distinguished. The results are stated in trajectory spaces endowed with topologies analogue to projective limit topologies. In this setting, the support of the law of the solution is also characterized. As a consequence, results on the law of the blow-up time and asymptotics when the noise converges to zero are obtained. An application to the transmission of solitary waves in fiber optics is also given.