Conditional moments in a critical age-dependent branching process

Abstract

Let X(t), N(t) respectively denote the number of cells alive at t and the total number of cells born by t in a critical age-dependent Bellman-Harris branching process.The asymptotic behavior of the conditional moments, for 0 < α ≦ 1, E(Nn(αt) | X(t) > 0), E(Nn(t) |X(αt) > 0), is obtained.