Gaps in discrete random samples

Prelegent(ci)

Paweł Hitczenko

Afiliacja

Drexel University

Termin

6 grudnia 2012 12:15

Pokój

p. 3260

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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For a sequence of independent and identically distributed random variables with values in the set of non-negative integers we investigate the number of gaps and the length of the longest gap in the set of the first n values. We obtain necessary and sufficient conditions in terms of the tail sequence for the gaps to vanish asymptotically (almost surely or in probability) as n goes to infinity.

We also give a sufficient condition for  the length of the longest gap to tend to infinity in probability.

This is based on a joint work with Rudolf Gruebel from Leibniz Universitaet Hannover.

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