Practical drift conditions for subgeometric rates of convergence

• 成果类型: Article
• 署名作者: Douc, R; Fort, G; Moulines, E; Soulier, P
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; IMT - Institut Mines-Telecom; IMT Atlantique; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite Paris Saclay
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000323
• 发表日期: 2004
• 页码: 1353-1377
• 关键词: Ergodicity; hastings

摘要

We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a psi-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts [Anti. Appl. Probab. 12 (2002) 224-247] for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic unit root models and multidimensional random walk Hastings-Metropolis algorithms.