Bernoulli

  • Bernoulli
  • Volume 19, Number 4 (2013), 1419-1448.

Clustering of Markov chain exceedances

Sidney I. Resnick and David Zeber

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Abstract

The tail chain of a Markov chain can be used to model the dependence between extreme observations. For a positive recurrent Markov chain, the tail chain aids in describing the limit of a sequence of point processes $\{N_{n},n\geq1\}$, consisting of normalized observations plotted against scaled time points. Under fairly general conditions on extremal behaviour, $\{N_{n}\}$ converges to a cluster Poisson process. Our technique decomposes the sample path of the chain into i.i.d. regenerative cycles rather than using blocking argument typically employed in the context of stationarity with mixing.

Article information

Source
Bernoulli, Volume 19, Number 4 (2013), 1419-1448.

Dates
First available in Project Euclid: 27 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1377612859

Digital Object Identifier
doi:10.3150/12-BEJSP08

Mathematical Reviews number (MathSciNet)
MR3102909

Zentralblatt MATH identifier
1284.60106

Citation

Resnick, Sidney I.; Zeber, David. Clustering of Markov chain exceedances. Bernoulli 19 (2013), no. 4, 1419--1448. doi:10.3150/12-BEJSP08. https://projecteuclid.org/euclid.bj/1377612859


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