Moments of general time dependent branching processes with applications (Q2330063)

The present paper is devoted to the study of some properties of Crump-Mode-Jagers (CMJ) processes. It gives conditions sufficient for a suitably scaled CMJ process to have finite kth moments, uniformly in \(t\geq 0\). This result is applied to the problem of describing the asymptotic behaviour of the maximal degree in a recently introduced random graph process evolving in continuous time and driven by time-dependent branching dynamics. It is concluded that the maximal degree has the same asymptotic order of magnitude as the degree of an arbitrary vertex.