Long-range dependence of Markov renewal processes

R. A. Vesilo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

This paper examines long-range dependence (LRD) and asymptotic properties of Markov renewal processes generalizing results of Daley for renewal processes. The Hurst index and discrepancy function, which is the difference between the expected number of arrivals in (0, t] given a point at 0 and the number of arrivals in (0, t] in the time stationary version, are examined in terms of the moment index. The moment index is the supremum of the set of r > 0 such that the rth moment of the first return time to a state is finite, employing the solidarity results of Sgibnev. The results are derived for irreducible, regular Markov renewal processes on countable state spaces. The paper also derives conditions to determine the moment index of the first return times in terms of the Markov renewal kernel distribution functions of the process.

Original languageEnglish
Pages (from-to)155-171
Number of pages17
JournalAustralian and New Zealand Journal of Statistics
Volume46
Issue number1
Publication statusPublished - Mar 2004

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