24 citations · 195 across the 74 of their papers we have counts for
6 papers · 2 filters
Renewal theory for iterated perturbed random walks on a general branching process tree: intermediate generations
Vladyslav Bohun, Alexander Iksanov, Alexander Marynych +1
Let be independent identically distributed random vectors with arbitrarily dependent positive components. We call a (globally) perturbed random walk a…
On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking II
Alexander Iksanov, Alexander Marynych, Igor Samoilenko
A nested occupancy scheme in random environment is a generalization of the classical Karlin infinite balls-in-boxes occupancy scheme in random environment (with random probabilitie…
On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking I
Dariusz Buraczewski, Bohdan Dovgay, Alexander Iksanov
Consider a weighted branching process generated by the lengths of intervals obtained by stick-breaking of unit length (a.k.a. the residual allocation model) and associate with each…
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…
A Brownian weak limit for the least common multiple of a random m-tuple of integers
Dariusz Buraczewski, Alexander Iksanov, Alexander Marynych
Let be a set picked uniformly at random among all -elements subsets of . We provide a pathwise construction of the collection $(B_n(m))_{1\leq m\leq n…
On the derivative martingale in a branching random walk
Dariusz Buraczewski, Alexander Iksanov, Bastien Mallein
We work under the A\"ıdékon-Chen conditions which ensure that the derivative martingale in a supercritical branching random walk on the line converges almost surely to a nondegener…