In the classical occupancy problem one puts balls in boxes, and each ball is independently assigned to any fixed box with probability . It is well known that, if we consider the random number of balls required to have all the boxes filled with at least one ball, the sequence converges to 1 in probability. Here we present the large deviation principle associated to this convergence. We also discuss the use of the Gärtner Ellis Theorem for the proof of some parts of this large deviation principle

Giuliano, R., Macci, C. (2013). On the asymptotic behavior of a sequence of random variables of interest in the classical occupancy problem. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 87, 31-40.

On the asymptotic behavior of a sequence of random variables of interest in the classical occupancy problem

MACCI, CLAUDIO
2013-01-01

Abstract

In the classical occupancy problem one puts balls in boxes, and each ball is independently assigned to any fixed box with probability . It is well known that, if we consider the random number of balls required to have all the boxes filled with at least one ball, the sequence converges to 1 in probability. Here we present the large deviation principle associated to this convergence. We also discuss the use of the Gärtner Ellis Theorem for the proof of some parts of this large deviation principle
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Giuliano, R., Macci, C. (2013). On the asymptotic behavior of a sequence of random variables of interest in the classical occupancy problem. THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 87, 31-40.
Giuliano, R; Macci, C
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/86471
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