A study of counts of Bernoulli strings via conditional Poisson processes
| dc.creator | Huffer, Fred W. | |
| dc.creator | Sethuraman, Jayaram | |
| dc.creator | Sethuraman, Sunder | |
| dc.date | 2008-01-14 | |
| dc.date.accessioned | 2026-07-07T08:54:21Z | |
| dc.date.available | 2026-07-07T08:54:21Z | |
| dc.description | We say that a string of length $d$ occurs, in a Bernoulli sequence, if a success is followed by exactly $(d-1)$ failures before the next success. The counts of such $d$-strings are of interest, and in specific independent Bernoulli sequences are known to correspond to asymptotic $d$-cycle counts in random permutations. In this note, we give a new framework, in terms of conditional Poisson processes, which allows for a quick characterization of the joint distribution of the counts of all $d$-strings, in a general class of Bernoulli sequences, as certain mixtures of the product of Poisson measures. This general class includes all Bernoulli sequences considered before, as well many new sequences. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0801.2115 | |
| dc.identifier | http://arxiv.org/abs/0801.2115 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145904 | |
| dc.subject | Probability | |
| dc.subject | 60C05; 60K99 | |
| dc.title | A study of counts of Bernoulli strings via conditional Poisson processes | |
| dc.type | text |