Taiwanese Journal of Mathematics

UNIFORM CLT FOR MARKOV CHAINS WITH A COUNTABLE STATE SPACE

Tsung-Hsi Tsai

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Abstract

We prove a uniform CLT for Markov chains for functions dominated by a function in a $L^{2}$-space. Using empirical process CLT's for stationary sequences satisfying a variety of mixing conditions one can obtain similar results. However, our conditions are less restrictive than those required for a mixing process application to these problems, and an example is given to these differences.

Article information

Source
Taiwanese J. Math., Volume 1, Number 4 (1997), 481-498.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406124

Digital Object Identifier
doi:10.11650/twjm/1500406124

Mathematical Reviews number (MathSciNet)
MR1486567

Zentralblatt MATH identifier
0898.60036

Subjects
Primary: 60F05: Central limit and other weak theorems 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Markov chain regenerative process empirical process uniform CLT.

Citation

Tsai, Tsung-Hsi. UNIFORM CLT FOR MARKOV CHAINS WITH A COUNTABLE STATE SPACE. Taiwanese J. Math. 1 (1997), no. 4, 481--498. doi:10.11650/twjm/1500406124. https://projecteuclid.org/euclid.twjm/1500406124


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