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**Hurst index of functions of long-range-dependent Markov chains.**
*(English)*
Zbl 1266.60127

Recall that a positive recurrent, aperiodic Markov chain is said to have long-range dependence (LRD) if the indicator function of a particular state has the LRD property. It can be shown that this is equivalent to the return time distribution of that state having infinite variance. The authors study whether there are other instantaneous functions of such a Markov chain that exhibit LRD. They formulate conditions which ensure that the function of the Markov chain inherits the same degree of LRD as the underlying Markov chain. Detailed examples from queueing networks, source compression and finance are discussed.

Reviewer: Almut Veraart (London)

### MSC:

60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |

68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |

68P30 | Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science) |

91G70 | Statistical methods; risk measures |

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\textit{B. Oğuz} and \textit{V. Anantharam}, J. Appl. Probab. 49, No. 2, 451--471 (2012; Zbl 1266.60127)

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