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2007 Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.
Dan Spitzner, Thomas Boucher
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Electron. Commun. Probab. 12: 120-133 (2007). DOI: 10.1214/ECP.v12-1262

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.

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Dan Spitzner. Thomas Boucher. "Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.." Electron. Commun. Probab. 12 120 - 133, 2007. https://doi.org/10.1214/ECP.v12-1262

Information

Accepted: 24 April 2007; Published: 2007
First available in Project Euclid: 6 June 2016

zbMATH: 1128.60062
MathSciNet: MR2300221
Digital Object Identifier: 10.1214/ECP.v12-1262

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