Limit theorem for

V. A. Vatutin   ; V. A. Topchii

Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 461-484

Résumé

A continuous time branching random walk on the lattice $Z$ is considered in which individuals may produce children at the origin only. Assuming that the underlying Markov random walk is homogeneous and symmetric and the offspring reproduction law is critical, we describe the asymptotic behavior as $t\to\infty$ of the conditional distribution of the two-dimensional vector $(\zeta(t), \mu (t))$ (scaled in an appropriate way), where $\zeta (t)$ and $\mu(t)$ are the numbers of individuals at the origin and outside the origin at moment $t$ given $\zeta(t)>0$.

Détail

Keywords: critical Bellman–Harris branching process with two types of individuals, inhomogeneous branching random walk on the lattice of real line, limit theorems.

Bibliographie

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