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June 2012 Hurst index of functions of long-range-dependent Markov chains
Barlas Oğuz, Venkat Anantharam
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J. Appl. Probab. 49(2): 451-471 (June 2012). DOI: 10.1239/jap/1339878798

Abstract

A positive recurrent, aperiodic Markov chain is said to be long-range dependent (LRD) when the indicator function of a particular state is LRD. This happens if and only if the return time distribution for that state has infinite variance. We investigate the question of whether other instantaneous functions of the Markov chain also inherit this property. We provide conditions under which the function has the same degree of long-range dependence as the chain itself. We illustrate our results through three examples in diverse fields: queueing networks, source compression, and finance.

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Barlas Oğuz. Venkat Anantharam. "Hurst index of functions of long-range-dependent Markov chains." J. Appl. Probab. 49 (2) 451 - 471, June 2012. https://doi.org/10.1239/jap/1339878798

Information

Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1266.60127
MathSciNet: MR2977807
Digital Object Identifier: 10.1239/jap/1339878798

Subjects:
Primary: 60J10
Secondary: 68M20, 68P30, 91G70

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 2 • June 2012
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