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The tail chain of a Markov chain can be used to model the dependence betweenextreme observations. For a positive recurrent Markov chain, the tail chainaids in describing the limit of a sequence of point processes $\{N_n,n\geq1\}$,consisting of normalized observations plotted against scaled time points. Underfairly general conditions on extremal behaviour, $\{N_n\}$ converges to acluster Poisson process. Our technique decomposes the sample path of the chaininto i.i.d. regenerative cycles rather than using blocking argument typicallyemployed in the context of stationarity with mixing.

Clustering of Markov chain exceedances