24 citations · 99 across the 51 of their papers we have counts for
7 papers · 1 filter
Random Walks in the High-Dimensional Limit I: The Wiener Spiral
Zakhar Kabluchko, Alexander Marynych
We prove limit theorems for random walks with steps in the -dimensional Euclidean space as both and tend to infinity. One of our results states that the path of such…
Limit theorems for random Dirichlet series
Dariusz Buraczewski, Congzao Dong, Alexander Iksanov +1
We prove a functional limit theorem in a space of analytic functions for the random Dirichlet series , properly scaled and nor…
Mod- convergence of Stirling distributions and limit theorems for zeros of their generating functions
Zakhar Kabluchko, Alexander Marynych, Helmut Pitters
We study mod- convergence of several probability distributions on the set of positive integers that involve Stirling numbers of both kinds and, as a consequence, derive various…
Limit theorems for discounted convergent perpetuities II
Alexander Iksanov, Alexander Marynych, Anatolii Nikitin
Let , be independent identically distributed -valued random vectors. Assuming that has zero mean and finite variance and imposin…
Solutions of kinetic-type equations with perturbed collisions
Dariusz Buraczewski, Piotr Dyszewski, Alexander Marynych
We study a class of kinetic-type differential equations , where is an inhomogeneous smoothing transfor…
Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree
Alexander Iksanov, Alexander Marynych, Bohdan Rashytov
Consider a general branching process, a.k.a. Crump-Mode-Jagers process, generated by a perturbed random walk , , . Here, , $(ξ_2, η_2),…