K. S. Ryadovkin, “On periodic branching random walks on <nobr>$\mathbf{Z}^d$</nobr> with infinite variance of jumps”, Teor. Veroyatnost. i Primenen., 2024, Volume 69, Issue 1,Pages <nobr>112

On periodic branching random walks on $\mathbf{Z}^d$ with infinite variance of jumps

K. S. Ryadovkin^ab

^a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: We consider periodic branching random walks with periodic branching sources. It is assumed that the transition intensities of the random walk satisfy some symmetry conditions and obey a condition which ensures infinite variance of jumps. In this case, we obtain the leading term for the asymptotics of the mean population size of particles at an arbitrary point of the lattice for large time.

Keywords: branching random walk, periodic perturbation, heavy tail, asymptotic behavior.

Received: 04.10.2021

DOI: 10.4213/tvp5533