@article{ECP1262,
author = {Dan Spitzner and Thomas Boucher},
title = {Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {12},
year = {2007},
keywords = {General state space Markov chains; \$f\$-regularity; Markov chain central limit theorem; Drazin inverse; fundamental matrix; asymptotic variance},
abstract = {We consider a $\psi$-irreducible, discrete-time Markov chain on a general state space with transition kernel $P$. Under suitable conditions on the chain, kernels can be treated as bounded linear operators between spaces of functions or measures and the Drazin inverse of the kernel operator $I - P$ exists. The Drazin inverse provides a unifying framework for objects governing the chain. This framework is applied to derive a computational technique for the asymptotic variance in the central limit theorems of univariate and higher-order partial sums. Higher-order partial sums are treated as univariate sums on a `sliding-window' chain. Our results are demonstrated on a simple AR(1) model and suggest a potential for computational simplification.},
pages = {no. 13, 120-133},
issn = {1083-589X},
doi = {10.1214/ECP.v12-1262},
url = {http://ecp.ejpecp.org/article/view/1262}}