Vladimir Vatutin: Limit Theorems for a Catalytic Branching Random Walk

This is a joint work with V.A.Topchii and E. B.Yarovaya.

We consider a continuous time branching random walk on the lattice $Z$ in which individuals may produce children at the origin only. Assuming that the underlying random walk is symmetric and the offspring reproduction law is critical we find the asymptotic behavior of the survival probability of the process at time $t$ as $t\rightarrow \infty$ and the probability that the number of individuals at the origin at time $t$ is positive. We also prove a Yaglom type conditional limit theorem for the total number of particles existing at time $t.$

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