13 citations · 14 across the 14 of their papers we have counts for
19 papers
Asymptotic fluctuations in supercritical multi-type Crump-Mode-Jagers processes
Konrad Kolesko, Alicja Kołodziejska, 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, Konrad Kolesko +1
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…
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 …
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.…
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 , …
Limit theorems for discrete multitype branching processes counted with a characteristic
Konrad Kolesko, Ecaterina Sava-Huss
For a discrete time multitype supercritical Galton-Watson process and corresponding genealogical tree , we associate a new discrete time proce…
Asymptotic fluctuations in supercritical Crump-Mode-Jagers processes
Alexander Iksanov, Konrad Kolesko, Matthias Meiners
Consider a supercritical Crump--Mode--Jagers process counted with a random characteristic . Nerman's celebrated law of large numbers [Z. Wahrsch. V…
Gaussian fluctuations and a law of the iterated logarithm for Nerman's martingale in the supercritical general branching process
Alexander Iksanov, Konrad Kolesko, Matthias Meiners
In his, by now, classical work from 1981, Nerman made extensive use of a crucial martingale to prove convergence in probability, in mean and almost surely, of su…
Solutions to kinetic-type evolution equations: beyond the boundary case
Dariusz Buraczewski, Konrad Kolesko, Matthias Meiners
We study the asymptotic behavior as of a time-dependent family of probability measures on solving the kinetic-type evolution equation…
Absolute continuity of the martingale limit in branching processes in random environment
Ewa Damek, Nina Gantert, Konrad Kolesko
We consider a supercritical branching process in a stationary and ergodic random environment . Due to the martingale convergence theorem, it is known that th…
Fluctuations of Biggins' martingales at complex parameters
Alexander Iksanov, Konrad Kolesko, Matthias Meiners
The long-term behavior of a supercritical branching random walk can be described and analyzed with the help of Biggins' martingales, parametrized by real or complex numbers. The st…
Stable-like fluctuations of Biggins' martingales
Alexander Iksanov, Konrad Kolesko, Matthias Meiners
Let be Biggins' martingale associated with a supercritical branching random walk, and let be its almost sure limit. Under a natural condition…
Convergence of complex martingales in the branching random walk: the boundary
Konrad Kolesko, Matthias Meiners
Biggins [Uniform convergence of martingales in the branching random walk. {\em Ann. Probab.}, 20(1):137--151, 1992] proved local uniform convergence of additive martingales in -…
Local fluctuations of critical Mandelbrot cascades
Dariusz Buraczewski, Piotr Dyszewski, Konrad Kolesko
We investigate so-called generalized Mandelbrot cascades at the freezing (critical) temperature. It is known that, after a proper rescaling, a~sequence of multiplicative cascades c…
Moment estimates for chaoses generated by symmetric random variables with logarithmically convex tails
Konrad Kolesko, Rafał Latała
We derive two-sided estimates for random multilinear forms (random chaoses) generated by independent symmetric random variables with logarithmically concave tails. Estimates are ex…
Fixed Points of the Multivariate Smoothing Transform: The Critical Case
Konrad Kolesko, Sebastian Mentemeier
Given a sequence of random matrices with nonnegative entries, suppose there is a random vector with nonnegative entries, such that $ \sum_{i \ge…
Brownian Motion on graph-like spaces
Agelos Georgakopoulos, Konrad Kolesko
We construct Brownian motion on a wide class of metric spaces similar to graphs, and show that its cover time admits an upper bound depending only on the length of the space.
Linear stochastic equations in the critical case
Dariusz Buraczewski, Konrad Kolesko
We consider solutions of the stochastic equation , where is a random natural number, and are random positive numbers and $X_i…