Abstract
A duality is made explicit between K-records of i.i.d sequences of observations and records in the F α-scheme. Via the Sakhanenko Lemma, we establish strong invariance principles for partial sums of independent random variables. We consider as applications of our main results the case of K-records. Afterwards, by making use of strong approximations of Markov chains, we establish invariance principles for records in a dual model: the F α-scheme. For both models limit results related to numbers of records are given.
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