On an Approximation Formula for the Extremal Index in a Markov Chain
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چکیده
In a previous paper, Smith and Weissman have considered estimators of the extremal index of a stationary stochastic process, and have shown that the theoretical properties of these estimators depend on an approximation formula for the extremal index. However, the derivation of this formula was entirely heuristic except for one very special case. In this paper, it is argued that the formula is valid for a broad class of processes, namely processes which are defined on a geometrically ergodic Harris Markov chain.
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تاریخ انتشار 1992