期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2015
卷号：XII
页码：491-532
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：The aim of this paper is to provide a simple model for describing speculativedynamics and to focus on the study of some associated quantities of interest.Starting from a description of individual speculative behaviors, we build a secondorder non-reversible Markov process, which after simple transformations can beviewed as a turning two-dimensional Gaussian process. Then, our main problemis to obtain some bounds for the persistence rate relative to the return time to agiven level. We prove with both spectral and probabilistic methods that this rateis almost proportional to the turning frequency ! of the model and provide someexplicit bounds. The persistence rate being strongly linked to the quasi-stationarydistribution of the problem, we also prove its existence. The main results are establishedwith a careful manipulation of a strongly degenerate hypoelliptic secondorder Markov operator, which signi cantly complicates the spectral analysis.
关键词：Speculative dynamics; Persistence rate; Gaussian Process; Di usion;Bridge; Quasi-stationary Distribution.
