Some applications of the Mellin transform to branching processes
| dc.creator | Angerer, Wolfgang P. | |
| dc.date | 2007-06-18 | |
| dc.date | 2008-04-16 | |
| dc.date.accessioned | 2026-07-07T09:32:33Z | |
| dc.date.available | 2026-07-07T09:32:33Z | |
| dc.description | We introduce a Mellin transform of functions which live on all of $\bR$ and discuss its applications to the limiting theory of Bellman-Harris processes, and specifically Luria-Delbrück processes. More precisely, we calculate the life-time distribution of particles in a Bellman-Harris process from their first-generation offspring and limiting distributions, and prove a formula for the Laplace transform of the distribution of types in a Luria-Delbrück process in the Mittag-Leffler limit. As a by-product, we show how to easily derive the (classical) Mellin transforms of certain stable probability distributions from their Fourier transform. | |
| dc.description | Proof of Theorem 6 revised; minor errors corrected | |
| dc.identifier | https://arxiv.org/abs/0706.2638 | |
| dc.identifier | http://arxiv.org/abs/0706.2638 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158817 | |
| dc.subject | Probability | |
| dc.subject | 44A05; 60J80 | |
| dc.title | Some applications of the Mellin transform to branching processes | |
| dc.type | text |