8 papers
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 tail behavior of infinite sums of independent indicators
Alexander Iksanov, Valeriya Kotelnikova
Let be an infinite sum of the indicators of independent events. We investigate a precise (as opposed to logarithmic) first-order asymptotic behavior of th…
First passage times for decoupled random walks
Alexander Iksanov, Zakhar Kabluchko, Vitali Wachtel
Motivated by a connection to the infinite Ginibre point process, decoupled random walks were introduced in a recent article Alsmeyer, Iksanov and Kabluchko (2025). The decoupled ra…
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…