Limit theorem for
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 461-484
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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 $\zeta(t)>0$.
Keywords:
critical Bellman–Harris branching process with two types of individuals, inhomogeneous branching random walk on the lattice of real line, limit theorems.
@article{TVP_2004_49_3_a2,
author = {V. A. Vatutin and V. A. Topchii},
title = {Limit theorem for},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {461--484},
publisher = {mathdoc},
volume = {49},
number = {3},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a2/}
}
V. A. Vatutin; V. A. Topchii. Limit theorem for. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 461-484. http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a2/