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August 1997 On independence of $k$-record processes: Ignatov's theorem revisited
Yi-Ching Yao
Ann. Appl. Probab. 7(3): 815-821 (August 1997). DOI: 10.1214/aoap/1034801255


For an infinite sequence of independent and identically distributed (i.i.d.) random variables, the k-record process consists of those terms that are the kth largest at their appearance. Ignatov's theorem states that the k-record processes, $k = 1, 2, \dots ,$ are i.i.d. A new proof is given which is based on a "continualization" argument. An advantage of this fairly simple approach is that Ignatov's theorem can be stated in a more general form by allowing for different tiebreaking rules. In particular, three tiebreakers are considered and shown to be related to Bernoulli, geometric and Poisson distributions.


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Yi-Ching Yao. "On independence of $k$-record processes: Ignatov's theorem revisited." Ann. Appl. Probab. 7 (3) 815 - 821, August 1997.


Published: August 1997
First available in Project Euclid: 16 October 2002

zbMATH: 0888.60041
MathSciNet: MR1459272
Digital Object Identifier: 10.1214/aoap/1034801255

Primary: 60G55

Keywords: Poisson process , Record values

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.7 • No. 3 • August 1997
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