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

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.