Open Access
September 2013 Clustering of Markov chain exceedances
Sidney I. Resnick, David Zeber
Bernoulli 19(4): 1419-1448 (September 2013). DOI: 10.3150/12-BEJSP08


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.


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Sidney I. Resnick. David Zeber. "Clustering of Markov chain exceedances." Bernoulli 19 (4) 1419 - 1448, September 2013.


Published: September 2013
First available in Project Euclid: 27 August 2013

zbMATH: 1284.60106
MathSciNet: MR3102909
Digital Object Identifier: 10.3150/12-BEJSP08

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

Vol.19 • No. 4 • September 2013
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