The Bernoulli sieve revisited

Details The Bernoulli sieve revisited The Bernoulli sieve revisited

2008-01-30

arxiv.org/abs/0801.4725v2

Annals of Applied Probability 2009, Vol. 19, No. 4, 1634-1655

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP592 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP592

We consider an occupancy scheme in which "balls" are identified with $n$ points sampled from the standard exponential distribution, while the role of "boxes" is played by the spacings induced by an independent random walk with positive and nonlattice steps. We discuss the asymptotic behavior of five quantities: the index $K_n^*$ of the last occupied box, the number $K_n$ of occupied boxes, the number $K_{n,0}$ of empty boxes whose index is at most $K_n^*$, the index $W_n$ of the first empty box and the number of balls $Z_n$ in the last occupied box. It is shown that the limiting distribution of properly scaled and centered $K_n^*$ coincides with that of the number of renewals not exceeding $\log n$. A similar result is shown for $K_n$ and $W_n$ under a side condition that prevents occurrence of very small boxes. The condition also ensures that $K_{n,0}$ converges in distribution. Limiting results for $Z_n$ are established under an assumption of regular variation.

Affiliated with

Also associated with

No associations

Rating

The Bernoulli sieve revisited does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Bernoulli sieve revisited, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Bernoulli sieve revisited will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-122266