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Hurst Index of Functions of Long-Range-Dependent Markov Chains

Part of: Theory of data Computer system organization Mathematical finance Markov processes

Published online by Cambridge University Press:  04 February 2016

Barlas Oğuz  and
Venkat Anantharam
Barlas Oğuz*
Affiliation:
University of California, Berkeley
Venkat Anantharam*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA.
∗ Postal address: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA.
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Abstract

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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.

Keywords

Markov chainlong-range dependenceHurst index

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 68M20: Performance evaluation; queueing; scheduling 68P30: Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) 91G70: Statistical methods, econometrics
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 451 - 471
Copyright
© Applied Probability Trust 

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