A. Iksanov

activity

20232026

collaborators

Showing math.PRShow all

10 papers · 1 filter

math.PR2026

On tail behavior of infinite sums of independent indicators

Alexander Iksanov, Valeriya Kotelnikova

Let $Y = \sum_{k \geq 1} 1_{A_{k}}$ be an infinite sum of the indicators of independent events. We investigate a precise (as opposed to logarithmic) first-order asymptotic behavior of th…

math.PR2026

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…

math.PR2025

Limit theorems for decoupled renewal processes

Congzao Dong, Iryna Feshchenko, Alexander Iksanov

The decoupled standard random walk is a sequence of independent random variables $(S^_{n})_{n \geq 1}$ , in which $S^_{n}$ has the same distribution as the position at time $n$ o…

math.PR2025

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…

math.PR2025

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 $J_{1}$ -topology for successive Lebesgue-Stieltjes convolutions of nondecreasing stochastic processe…

math.PR2025

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…

math.PR2025

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 $(S^_{n})_{n \geq 1}$ such that, for each $n \geq 1$ , the distribution of $S^_{n}$ is the same…

math.PR2025

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 $f$ is a Besicovitch almo…

math.PR2023

On multidimensional locally perturbed standard random walks

Congzao Dong, Alexander Iksanov, Andrey Pilipenko

Let $d$ be a positive integer and $A$ a set in $Z^{d}$ , which contains finitely many points with integer coordinates. We consider $X$ a standard random walk perturbed on the…

math.PR2023

On a discrete approximation of a skew stable Lévy process

Congzao Dong, Oleksandr Iksanov, Andrey Pilipenko

Iksanov and Pilipenko (2023) defined a skew stable Lévy process as a scaling limit of a sequence of perturbed at $0$ symmetric stable Lévy processes (continuous-time processes). He…