RATES OF CONVERGENCE OF SOME MULTIVARIATE MARKOV CHAINS WITH POLYNOMIAL EIGENFUNCTIONS

• 成果类型: Article
• 署名作者: Khare, Kshitij; Zhou, Hua
• 署名单位: Stanford University; University of California System; University of California Los Angeles; University of California Los Angeles Medical Center; David Geffen School of Medicine at UCLA
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP562
• 发表日期: 2009
• 页码: 737-777
• 关键词: orthogonal polynomials; stationarity; times; inequalities

摘要

We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our examples include the Moran model in population genetics and its variants in community ecology, the Dirichlet-multinomial Gibbs sampler, a class of generalized Bernoulli-Laplace processes, a generalized Ehrenfest urn model and the multivariate normal autoregressive process.