6 papers · 1 filter
Limit theorems for decoupled renewal processes
Congzao Dong, Iryna Feshchenko, Alexander Iksanov
The decoupled standard random walk is a sequence of independent random variables , in which has the same distribution as the position at time o…
Some central limit theorems for critical beta-splitting tree
Alexander Iksanov, Anatolii Nikitin, Roman Yakymiv
We further explore a connection initially unveiled in Iksanov (2025) between critical beta-splitting trees and infinite `balls-in-boxes' schemes. Using the connection, we derive a…
Functional limit theorems for random Lebesgue-Stieltjes convolutions
Alexander Iksanov, Wissem Jedidi
We prove joint functional limit theorems in the Skorokhod space equipped with the -topology for successive Lebesgue-Stieltjes convolutions of nondecreasing stochastic processe…
Limit theorems for random Dirichlet series with summation over primes, with an application to Rademacher random multiplicative functions
Congzao Dong, Alexander Iksanov
It is shown that two conjectures put forward in the recent article Iksanov and Kostohryz (2025) are true. Namely, we prove a functional central limit theorem (FCLT) and a law of th…
On local large deviations for decoupled random walks
Dariusz Buraczewski, Alexander Iksanov, Alexander Marynych
A decoupled standard random walk is a sequence of independent random variables such that, for each , the distribution of is the same…
Almost periodic stochastic processes with applications to analytic number theory
Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych
A classical fact of the theory of almost periodic functions is the existence of their asymptotic distributions. In probabilistic terms, this means that if is a Besicovitch almo…