The Annals of Applied Probability

Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions

Kshitij Khare and Hua Zhou

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Abstract

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.

Article information

Source
Ann. Appl. Probab. Volume 19, Number 2 (2009), 737-777.

Dates
First available in Project Euclid: 7 May 2009

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1241702249

Digital Object Identifier
doi:10.1214/08-AAP562

Mathematical Reviews number (MathSciNet)
MR2521887

Zentralblatt MATH identifier
1171.60016

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J22: Computational methods in Markov chains [See also 65C40] 33C50: Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable

Keywords
Convergence rate Markov chains multivariate orthogonal polynomials

Citation

Khare, Kshitij; Zhou, Hua. Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions. Ann. Appl. Probab. 19 (2009), no. 2, 737--777. doi:10.1214/08-AAP562. http://projecteuclid.org/euclid.aoap/1241702249.


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