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A sufficiency property arising from the characterization of extremes of Markov chains. (English) Zbl 0955.60059

Summary: At extreme levels, it is known that for a particular choice of marginal distribution, transitions of a Markov chain behave like a random walk. For a broad class of Markov chains, we give a characterization for the step length density of the limiting random walk, which leads to an interesting sufficiency property. This representation also leads us to propose a new technique for kernel density estimation for this class of models.

MSC:

60G70 Extreme value theory; extremal stochastic processes
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