External Theory for Stochastic Processes.
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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The purpose of this paper is to provide an overview of the asymptotic distributional theory of extreme values for a wide class of dependent stochastic sequences and continuous parameter processes. The theory contains the standard classical extreme value results for maxima and extreme order statistics as special cases but is richer on account of the diverse behavior possible under dependence in both discrete and continuous time contexts. Emphasis is placed on stationary cases but other important classes e.g. Mark of sequences are included. Significant ideas and methods are described rather than details, and in particular the nature and role of important underlying point processes such as exceedances and upcrossings are emphasized. Applications are given to particular classes of process e.g. normal, moving average and connections with related theory such as convergence of sums are indicated.
- Statistics and Probability