Sums of i.i.d. random variables and an application to the explosion criterion for markov branching processes

Abstract

We give necessary and sufficient conditions for in terms of , where Sn is the sum of n i.i.d. random variables with values in]0, ∞[, and A ≧ 0. We use these results to give a probabilistic proof of the ‘explosion criterion' for continuous-time Markov branching processes, which is usually shown analytically.