6 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…
Maximal and minimal displacement of supercritical branching random walks on free products of groups
Robin Kaiser, Martin Klötzer, Martin Klötzer +2
We prove that the maximal and minimal displacement of branching random walks with mean offspring number on free products of finite groups grows linearly almost surely. More p…
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…
Gaussian fluctuations for the two urn model
Konrad Kolesko, Ecaterina Sava-Huss
We introduce a modification of the generalized Pólya urn model containing two urns and we study the number of balls of a given color , $J\in\mathbb{N}…