Branching random walk in Z^4 with branching at the origin only

Yueyun Hu (1) , Valentin Topchii (2) , Vladimir Vatutin (3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Omsk branch of Sobolev Institute of Mathematics
3 SMI | RAS - Steklov Mathematical Institute [Moscow]

For the critical branching random walk in $\mathbb{Z}^{4}$ with branching at the origin only we find the asymptotic behavior of the probability of the event that there are particles at the origin at moment $t\rightarrow \infty $ and prove a Yaglom type conditional limit theorem for the number of individuals at the origin given that there are particles at the origin.

Mots clés: Branching random walk

Domaines: Probabilités [math.PR]

Yueyun Hu, Valentin Topchii, Vladimir Vatutin. Branching random walk in Z^4 with branching at the origin only. 2010. ⟨hal-00492684⟩