The moment analysis of a branching random walk on a lattice with a single source (Q1594212)

The paper investigates the asymptotic behavior of the continuous-time branching random walk on \(Z^d, d\geq 1\), in which particles may produce children only at a fixed point (source) of the lattice. Assuming that the random walk is homogeneous, irreducible and with jumps having zero mean and finite varince, the authors investigate the limiting behavior of the integer moments of the total number of particles in the process and the integer moments of the number of particles at fixed points of the lattice. They show, in particular, that for the critical processes the asymptotic representations of the mentioned moments are essentially different for \(d=1,2,3,4\) and \(d\geq 5\).