2016/02/05 by Bernard Bercu, Bercu, Bernard, Adrien Richou +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1602.02092
openalex publication_date 2016/02/05 · arxiv created 2016/02/08 · arxiv updated 2016/02/09 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Our goal is to establish large deviations and concentration inequalities for the maximum likelihood estimator of the drift parameter of the Ornstein-Uhlenbeck process without tears. We propose a new strategy to establish large deviation results which allows us, via a suitable transformation, to circumvent the classical difficulty of non-steepness. Our approach holds in the stable case where the process is positive recurrent as well as in the unstable and explosive cases where the process is respectively null recurrent and transient. Notwithstanding of this trichotomy, we also provide new concentration inequalities for the maximum likelihood estimator.