On independence of $k$-record processes: Ignatov's theorem revisited
Yao, Yi-Ching
Ann. Appl. Probab., Tome 7 (1997) no. 1, p. 815-821 / Harvested from Project Euclid
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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.
Publié le : 1997-08-14
Classification:  Record values,  Poisson process,  60G55 
@article{1034801255,
     author = {Yao, Yi-Ching},
     title = {On independence of $k$-record processes: Ignatov's theorem
		 revisited},
     journal = {Ann. Appl. Probab.},
     volume = {7},
     number = {1},
     year = {1997},
     pages = { 815-821},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1034801255}
}

Yao, Yi-Ching. On independence of $k$-record processes: Ignatov's theorem
		 revisited. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp.  815-821. http://gdmltest.u-ga.fr/item/1034801255/