Central limit theorems and invariance principles are obtained for
additive functionals of a stationary ergodic Markov chain, say
$S_n = g(X_1)+ \cdots + g(X_n)$ where $E[g(X_1)]= 0$ and
$E[g(X_1)^2]<\infty$. The
conditions imposed restrict the moments of $g$ and the growth of the
conditional means $E(S_n|X_1)$. No other restrictions on the dependence
structure of the chain are required. When specialized to shift processes,the
conditions are implied by simple integral tests involving $g$.
@article{1019160258,
author = {Maxwell, Michael and Woodroofe, Michael},
title = {Central limit theorems for additive functionals of Markov
chains},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 713-724},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160258}
}
Maxwell, Michael; Woodroofe, Michael. Central limit theorems for additive functionals of Markov
chains. Ann. Probab., Tome 28 (2000) no. 1, pp. 713-724. http://gdmltest.u-ga.fr/item/1019160258/