SPIKING AND COLLAPSING IN LARGE NOISE LIMITS OF SDES
成果类型：
Article
署名作者：
Bernardin, Cedric; Chetrite, Raphael; Chhaibi, Reda; Najnudel, Joseph; Pellegrini, Clemnt
署名单位：
Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/22-AAP1819
发表日期：
2023
页码：
417-446
关键词：
摘要：
We analyze the strong noise limit of one-dimensional stochastic differ-ential equations (SDEs).Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an intriguing behavior. As the noise grows larger, the solutions exhibit locally a collapsing, that is to say, converge to pure jump processes very reminiscent of a metastability phenomenon. But surprisingly the limiting jump process is decorated by a spike process.We give a precise meaning to the convergence and completely prove these statements for a large class of one-dimensional diffusions, thanks to a robust strategy of proof.