DISCRETE STICKY COUPLINGS OF FUNCTIONAL AUTOREGRESSIVE PROCESSES

• 成果类型: Article
• 署名作者: Durmus, Alain; Eberle, Andreas; Enfroy, Aurelien; Guillin, Arnaud; Monmarche, Pierre
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; University of Bonn; Universite Paris Saclay; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2053
• 发表日期: 2024
• 页码: 5032-5075
• 关键词: perturbation-theory; markov-chains; CONVERGENCE; rates

摘要

In this paper, we provide bounds in Wasserstein and total variation distances between the distributions of the successive iterates of two functional autoregressive processes with isotropic Gaussian noise of the form Yk+1 = T gamma (Yk)+ gamma sigma 2Zk+1 and Yk+1 = T gamma ( Yk)+ gamma sigma 2 Zk+1. More precisely, we give nonasymptotic bounds on rho(L(Yk),L( Yk)), where rho is an appropriate weighted Wasserstein distance or a V-distance, uniformly in the parameter gamma , and on rho (pi gamma , pi gamma ), where pi gamma and pi gamma are the respective stationary measures of the two processes. The class of considered processes encompasses the Euler-Maruyama discretization of Langevin diffusions and its variants. The bounds we derive are of order gamma as gamma -* 0. To obtain our results, we rely on the construction of a discrete sticky Markov chain (W(gamma ) bounds the distance between an appropriate coupling of the two processes. We then establish stability and quantitative convergence results for this process uniformly on gamma . In addition, we show that it converges in distribution to the continuous sticky process studied in Howitt (Ph.D. thesis (2007)) and 2394). Finally, we apply our result to Bayesian inference of ODE parameters and numerically illustrate them on two particular problems.