V. Kotelnikova

activity

20212026

collaborators

4 papers

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.PR2023

A law of the iterated logarithm for small counts in Karlin's occupancy scheme

Alexander Iksanov, Valeriya Kotelnikova

In the Karlin infinite occupancy scheme, balls are thrown independently into an infinite array of boxes $1$ , $2, \dots$ , with probability $p_{k}$ of hitting the box $k$ . For $j,n\in\…

math.PR2022

Small counts in nested Karlin's occupancy scheme generated by discrete Weibull-like distributions

Alexander Iksanov, Valeriya Kotelnikova

A nested Karlin's occupancy scheme is a symbiosis of classical Karlin's balls-in-boxes scheme and a weighted branching process. To define it, imagine a deterministic weighted branc…

math.PR2021

A functional limit theorem for nested Karlin's occupancy scheme generated by discrete Weibull-like distributions

Alexander Iksanov, Zakhar Kabluchko, Valeriya Kotelnikova

Let $(p_{k})_{k \in N}$ be a discrete probability distribution for which the counting function $x \mapsto # {k \in N : p_{k} \geq 1/ x}$ belongs to the de Haan class $Π$ . C…