Harmonic continuous-time branching moments
| dc.creator | Piau, Didier | |
| dc.date | 2005-11-02 | |
| dc.date | 2007-02-14 | |
| dc.date.accessioned | 2026-07-07T07:46:37Z | |
| dc.date.available | 2026-07-07T07:46:37Z | |
| dc.description | We show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population $k$ is greater than a first threshold $m_1\ge1$. If, furthermore, $k$ is greater than a second threshold $m_2\ge m_1$, the normalized mean inverse population is at most $1/(k-m_2)$. We express $m_1$ and $m_2$ as explicit functionals of the reproducing distribution, we discuss some analogues for discrete time branching processes and link these results to the behavior of random products involving i.i.d. nonnegative sums. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051606000000493 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0511058 | |
| dc.identifier | http://arxiv.org/abs/math/0511058 | |
| dc.identifier | Annals of Applied Probability 2006, Vol. 16, No. 4, 2078-2097 | |
| dc.identifier | doi:10.1214/105051606000000493 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123888 | |
| dc.subject | Probability | |
| dc.subject | 60J80 (Primary) | |
| dc.title | Harmonic continuous-time branching moments | |
| dc.type | text |