The CLT for stationary Markov chains with trivial tail sigma field

Authors

Magda Peligrad, University of Cincinnati

Document Type

Lecture

Publication Date

9-28-2022

Abstract

In this talk we consider stationary Markov chains with trivial two-sided tail sigma field and present the tools leading to the following result: Any additive functional of such a Markov chain satisfies the central limit theorem provided the variance of partial sums divided by n is bounded. The method is based on martingale decomposition using a new idea involving conditioning with respect to both the past and the future of the chain. No assumption of irreducibility or aperiodicity is needed.

Relational Format

presentation

Recommended Citation

Peligrad, Magda, "The CLT for stationary Markov chains with trivial tail sigma field" (2022). Probability & Statistics Seminar. 27.
https://egrove.olemiss.edu/math_statistics/27