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pro vyhledávání: '"Kotelnikova, Valeriya"'
In the Karlin infinite occupancy scheme, balls are thrown independently into an infinite array of boxes $1$, $2,\ldots$, with probability $p_k$ of hitting the box $k$. For $j,n\in\mathbb{N}$, denote by $\mathcal{K}^*_j(n)$ the number of boxes contain
Externí odkaz:
http://arxiv.org/abs/2310.06087
We prove a law of the iterated logarithm (LIL) for an infinite sum of independent indicators parameterized by $t$ as $t\to\infty$. It is shown that if the expectation $b$ and the variance $a$ of the sum are comparable, then the normalization in the L
Externí odkaz:
http://arxiv.org/abs/2306.15027
Consider a Crump-Mode-Jagers process generated by an increasing random walk whose increments have finite second moment. Let $Y_k(t)$ be the number of individuals in generation $k\in \mathbb N$ born in the time interval $[0,t]$. We prove a law of the
Externí odkaz:
http://arxiv.org/abs/2212.13441
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 branching process in which weights of the first generation individuals are
Externí odkaz:
http://arxiv.org/abs/2203.08918
Let $(p_k)_{k\in\mathbb{N}}$ be a discrete probability distribution for which the counting function $x\mapsto \#\{k\in\mathbb{N}: p_k\geq 1/x\}$ belongs to the de Haan class $\Pi$. Consider a deterministic weighted branching process generated by $(p_
Externí odkaz:
http://arxiv.org/abs/2104.06948
Publikováno v:
Modern Stochastics: Theory & Applications; Mar2024, Vol. 11 Issue 2, p217-245, 29p
We prove a central limit theorem accompanied by the convergence of all exponential moments and a law of the iterated logarithm (LIL) for an infinite sum of independent indicators parameterized by $t$ as $t\to\infty$. It is shown that if the expectati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bc1aa9cbd476061708846c2afbc435a5
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