Rates of convergence for everywhere-positive Markov chains

J. R. Baxter, Jeffrey S. Rosenthal

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.

Original languageEnglish (US)
Pages (from-to)333-338
Number of pages6
JournalStatistics and Probability Letters
Volume22
Issue number4
DOIs
StatePublished - Mar 1995

Bibliographical note

Funding Information:
We thank Peter gosenthal for helpful discussions, and thank the referee for useful comments. This work was partially supported by NSF and by NSERC.

Keywords

  • Compact operator
  • Geometric convergence
  • Gibbs sampler
  • Hilbert-Schmidt condition
  • Markov chain
  • Monte Carlo
  • Stationary distribution

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