Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions

Details Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions

2009-06-23

arxiv.org/abs/0906.4242v1

Annals of Applied Probability 2009, Vol. 19, No. 2, 737-777

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP562 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP562

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.

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