On a Periodic Branching Random Walk on $\mathbf{Z}^{{d}}$ with an Infinite Variance of Jumps

Abstract

Theory of Probability &Its Applications, Volume 69, Issue 1, Page 88-98, May 2024.
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.