4 papers
Asymptotic fluctuations in supercritical multi-type Crump-Mode-Jagers processes
Konrad Kolesko, Alicja KoÅodziejska, Matthias Meiners
We consider an irreducible, supercritical multi-type general branching process (Crump-Mode-Jagers process) with finite type space, counted with random characteristic. We prove that…
Explosion of Crump-Mode-Jagers processes with critical immediate offspring
Gerold Alsmeyer, Konrad Kolesko, Matthias Meiners +1
We study the phenomenon of explosion in general (Crump-Mode-Jagers) branching processes, which refers to the event where an infinite number of individuals are born in finite time.…
Convergence of complex martingales in supercritical multi-type general branching processes in for
Konrad Kolesko, Matthias Meiners, Ivana Tomic
Nerman's martingale plays a central role in the law of large numbers for both, single- and multi-type, supercritical general branching processes. There are further, complex-valued…
Asymptotic expansions of solutions to Markov renewal equations and their application to general branching processes
Konrad Kolesko, Matthias Meiners, Ivana Tomic
We consider the Markov renewal equation for vector-valued functions and a matrix $\boldsymbolμ…