## Brazilian Journal of Probability and Statistics

### Boosting, downsizing and optimality of test functions of Markov chains

Thomas R. Boucher

#### Abstract

Test functions play an important role in Markov chain theory. Stability of a Markov chain can be demonstrated by constructing a test function of the chain that satisfies a stochastic drift criterion. The test function defines a class of functions of the process for which limit laws hold, yields bounds on the convergence of the Markov chain transition probabilities to the stationary distribution, and provides information concerning the mixing properties of the chain. Under certain conditions, these results can be improved by using a new test function derived from a known test function of a Markov chain.

#### Article information

Source
Braz. J. Probab. Stat., Volume 31, Number 3 (2017), 640-652.

Dates
Accepted: June 2016
First available in Project Euclid: 22 August 2017

https://projecteuclid.org/euclid.bjps/1503388832

Digital Object Identifier
doi:10.1214/16-BJPS327

Mathematical Reviews number (MathSciNet)
MR3693984

Zentralblatt MATH identifier
1378.60097

#### Citation

Boucher, Thomas R. Boosting, downsizing and optimality of test functions of Markov chains. Braz. J. Probab. Stat. 31 (2017), no. 3, 640--652. doi:10.1214/16-BJPS327. https://projecteuclid.org/euclid.bjps/1503388832

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