The distributions of cluster functionals of extreme events in a dTH-order Markov chain

The paper concerns the asymptotic distributions of cluster functionals of e xtreme events in a dth-order stationary Markov chain {X-n, n = 1,2,...} for which the joint distribution of (X-1,...,Xd+l) is absolutely continuous. U nder some distributional assumptions for {X-n}, we establish weak convergen ce for a class of cluster functionals and obtain representations for the as ymptotic distributions which are well suited for simulation. A number of ex amples important in applications are presented to demonstrate the usefulnes s of the results.