Occupation time fluctuation limits of infinite variance equilibrium branching systems
| dc.creator | Milos, Piotr | |
| dc.date | 2008-02-01 | |
| dc.date.accessioned | 2026-07-07T09:18:17Z | |
| dc.date.available | 2026-07-07T09:18:17Z | |
| dc.description | We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,α,β)$-branching particle system. It consists of particles moving according to a symmetric $α$-stable motion in $\mathbb{R}^d$. The branching law is in the domain of attraction of a (1+$β$)-stable law and the initial condition is an equilibrium random measure for the system (defined below). In the paper we treat separately the cases of intermediate $α/β<d<(1+β)α/β$, critical $d=(1+β)α/β$ and large $d>(1+β)α/β$ dimensions. In the most interesting case of intermediate dimensions we obtain a version of a fractional stable motion. The long-range dependence structure of this process is also studied. Contrary to this case, limit processes in critical and large dimensions have independent increments. | |
| dc.identifier | https://arxiv.org/abs/0802.0187 | |
| dc.identifier | http://arxiv.org/abs/0802.0187 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153971 | |
| dc.subject | Probability | |
| dc.subject | 60F17, 60J80 | |
| dc.title | Occupation time fluctuation limits of infinite variance equilibrium branching systems | |
| dc.type | text |