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Ignatov's theorem: a new and short proof

Published online by Cambridge University Press:  14 July 2016

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.

Type
Part 6 - The Analysis of Stochastic Phenomena
Copyright
Copyright © Applied Probability Trust 1988 

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