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Scheduled maxima sequences

Published online by Cambridge University Press:  14 July 2016

Joseph G. Deken
Joseph G. Deken*
Affiliation:
Princeton University
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Abstract

We define a vector-valued scheduled maxima sequence M by considering simultaneously the maxima of several i.i.d. sequences, with the number of observations considered from each sequence at any time determined by a random scheduling sequence J. It is shown that the max-min (vector) sequence derived from i.i.d. can be represented as a mixture of scheduled maxima sequences, giving results for this sequence and the range A functional limit theorem for the scheduled maxima sequence shows convergence to independent extremal processes. Embedding in a scheduled extremal process gives strong laws, central limit theorems, and laws of the iterated logarithm for the record time of the scheduled maxima sequence, and hence for the max-min sequence and the range.

Keywords

MAXIMAMINIMARANGEWEAK CONVERGENCEFUNCTIONAL LIMIT THEOREMSEXTREMAL PROCESSESRECORD VALUESPOISSON PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 543 - 551
Copyright
Copyright © Applied Probability Trust 1978 

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