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Ignatov's theorem: a new and short proof

Published online by Cambridge University Press:  14 July 2016

Ron Engelen ,
Paul Tommassen  and
Wim Vervaat
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Abstract

By Ignatov's theorem the sets of values in an i.i.d. sequence that are the kth largest at their appearance (k = 1, 2, ···) are supports of i.i.d. Poisson processes. The present paper contains an elementary and short proof for the case where the underlying distribution function F is discrete, and then extends the result to general F.

Keywords

IGNATOV'S THEOREMRECORD VALUESPOISSON PROCESS
Type
Part 6 - The Analysis of Stochastic Phenomena
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 229 - 236
Copyright
Copyright © Applied Probability Trust 1988 

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References

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