Bernoulli

  • Bernoulli
  • Volume 9, Number 4 (2003), 559-578.

Necessary conditions for geometric and polynomial ergodicity of random-walk-type

Søren F. Jarner and Richard L. Tweedie

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Abstract

We give necessary conditions for geometric and polynomial convergence rates of randomwalk- type Markov chains to stationarity in terms of existence of exponential and polynomial moments of the invariant distribution and the Markov transition kernel. These results complement the use of Foster-Lyapunov drift conditions for establishing geometric and polynomial ergodicity. For polynomially ergodic Markov chains, the results allow us to derive exact rates of convergence and exact relations between the moments of the invariant distribution and the Markov transition kernel. In an application to Markov chain Monte Carlo we derive tight rates of convergence for symmetric random walk Metropolis.

Article information

Source
Bernoulli, Volume 9, Number 4 (2003), 559-578.

Dates
First available in Project Euclid: 15 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.bj/1066223269

Digital Object Identifier
doi:10.3150/bj/1066223269

Mathematical Reviews number (MathSciNet)
MR1996270

Zentralblatt MATH identifier
1043.60054

Keywords
geometric and polynomial moments Markov chains Metropolis algorithms

Citation

Jarner, Søren F.; Tweedie, Richard L. Necessary conditions for geometric and polynomial ergodicity of random-walk-type. Bernoulli 9 (2003), no. 4, 559--578. doi:10.3150/bj/1066223269. https://projecteuclid.org/euclid.bj/1066223269


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