Sharpness of second moment criteria for branching and tree-indexed processes
| dc.creator | Pemantle, Robin | |
| dc.date | 2004-04-05 | |
| dc.date.accessioned | 2026-07-07T05:07:08Z | |
| dc.date.available | 2026-07-07T05:07:08Z | |
| dc.description | A class of branching processes in varying environments is exhibited which become extinct almost surely even though the means M_n grow fast enough so that sum M_n^{-1} is finite. In fact, such a process is constructed for every offspring distribution of infinite variance, and this establishes the converse of a previously known fact: that if a distribution has finite variance then sum M_n^{-1}=infty is equivalent to almost sure extinction. This has as an immediate consequence the converse to a theorem on equipolarity of Galton-Watson trees. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404090 | |
| dc.identifier | http://arxiv.org/abs/math/0404090 | |
| dc.identifier | Classical and modern branching processes, 257 - 262, IMA Vol. Math. Appl., 84, Springer (1997) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70739 | |
| dc.subject | Probability | |
| dc.title | Sharpness of second moment criteria for branching and tree-indexed processes | |
| dc.type | text |