%0 Journal Article
%T Clustering of Markov chain exceedances
%A Sidney I. Resnick
%A David Zeber
%J Statistics
%D 2012
%I arXiv
%R 10.3150/12-BEJSP08
%X 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.
%U http://arxiv.org/abs/1210.2314v2