On the Markov chain central limit theorem

Central and Local Limit Theories in Markov Dependent Random Variables

Bootstrap Central Limit Theorem for Chains of Infinite Order via Markov Approximations

We present a new approach to the bootstrap for chains of infinite order taking values on a finite alphabet. It is based on a sequential Bootstrap Central Limit Theorem for the sequence of canonical Markov approximations of the chain of infinite order. Combined with previous results on the rate of approximation this leads to a Central Limit Theorem for the bootstrapped estimator of the sample me...

A Central Limit Theorem for Iterated Random Functions

A central limit theorem is established for additive functions of a Markov chain that can be constructed as an iterated random function. The result goes beyond earlier work by relaxing the continuity conditions imposed on the additive function, and by relaxing moment conditions related to the random function. It is illustrated by an application to a Markov chain related to fractals.

The Central Limit Theorem for the Normalized Sums of Extended Sliding Block Codes from Sequences of Markov Chains with Time Delay

We extend the sliding block code in symbolic dynamics to transform two sequences of Markov chains with time delay. Under the assumption that chains are irreducible and aperiodic, we prove the central limit theorem (CLT) for the normalized sums of extended sliding block codes from two sequences of Markov chains. We apply the theorem to evaluations of bit error probabilities in asynchronous sprea...

Central Limit Theorems for Conditional Markov Chains

This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is established. The asymptotic variance can be estimated by resampling the latent states conditional on the observations. If the conditional means...