I. I. Lukashova, “Periodic branching random walk on <nobr>$\mathbf {Z}^d$</nobr> with immigration”, Zap. Nauchn. Sem. POMI, 2023, Volume 526,Pages <nobr>90

Periodic branching random walk on $\mathbf {Z}^d$ with immigration

I. I. Lukashova^ab

^a Euler International Mathematical Institute, St. Petersburg
^b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: We consider a continuous-time branching random walk with immigration on $\mathbf {Z}^d$ with branching sources located periodically. The asymptotic behavior of the mean number of particles at an arbitrary point is obtained for $t\to\infty$ in the supercritical and subcritical cases.

Key words and phrases: branching random walk, periodic perturbation, the direct integral decomposition.

UDC: 519.2

Received: 28.09.2023