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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 13 open journal systems 

Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.

Dan J. Spitzner, Department of Statistics (0439), Virginia Tech, Blacksburg, VA
Thomas R Boucher, Department of Mathematics, Plymouth State

We consider a ψ-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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Pages: 120-133

Published on: April 24, 2007

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Electronic Communications in Probability. ISSN: 1083-589X