Year: 2024
Type: preprint
Abstract: We study a critical multitype Bellman--Harris branching particle system in \(\mathbb R^N\) with a finite type space \(\mathbf K=\{1,\dots,K\}\). Particles of type \(I\) move according to a symmetric \(α_i\)-stable process, have non-arithmetic lifetimes with finite mean, and reproduce according to a critical offspring law whose mean matrix is irreducible and stochastic. The branching mechanism is assumed to be in the domain of attraction of a \((1+β)\)-stable law, with \(β\in(0,1]\). We prove that the particle system converges, as \(t\to\infty\), to a limiting random measure which is nonzero. We also show that the limiting population preserves the initial intensity measure. Thus, the system persists with full intensity. These results complement the local extinction results of Kevei and Lopez-Mimbela (2011) for critical multitype Bellman--Harris systems.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404304570