Strong Law of Large Numbers for branching diffusions
| dc.creator | Englander, Janos | |
| dc.creator | Harris, Simon C. | |
| dc.creator | Kyprianou, Andreas E. | |
| dc.date | 2007-09-03 | |
| dc.date.accessioned | 2026-07-07T08:27:18Z | |
| dc.date.available | 2026-07-07T08:27:18Z | |
| dc.description | Let $X$ be the branching particle diffusion corresponding to the operator $Lu+β(u^{2}-u)$ on $D\subseteq \mathbb{R}^{d}$ (where $β\geq 0$ and $β\not\equiv 0$). Let $λ_{c}$ denote the generalized principal eigenvalue for the operator $L+β$ on $D$ and assume that it is finite. When $λ_{c}>0$ and $L+β-λ_{c}$ satisfies certain spectral theoretical conditions, we prove that the random measure $\exp \{-λ_{c}t\}X_{t}$ converges almost surely in the vague topology as $t$ tends to infinity. This result is motivated by a cluster of articles due to Asmussen and Hering dating from the mid-seventies as well as the more recent work concerning analogous results for superdiffusions of \cite{ET,EW}. We extend significantly the results in \cite{AH76,AH77} and include some key examples of the branching process literature. As far as the proofs are concerned, we appeal to modern techniques concerning martingales and `spine' decompositions or `immortal particle pictures'. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/0709.0272 | |
| dc.identifier | http://arxiv.org/abs/0709.0272 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137224 | |
| dc.subject | Probability | |
| dc.subject | 60J60 | |
| dc.title | Strong Law of Large Numbers for branching diffusions | |
| dc.type | text |