A. Marynych

activity

20092026

most citedLimit theorems for the number of occupied boxes in the Bernoulli sieve

24 citations · 99 across the 51 of their papers we have counts for

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Showing 2012Show all

4 papers · 1 filter

math.PR2012★ 1 cited

Limit theorems for renewal shot noise processes with decreasing response functions

A. Iksanov, A. Marynych, M. Meiners

We consider shot noise processes $(X (t))_{t \geq 0}$ with deterministic response function $h$ and the shots occurring at the renewal epochs $0 = S_{0} < S_{1} < S_{2} ...$ of a zero-delay…

math.PR2012

Moment convergence of first-passage times in renewal theory

Alexander Iksanov, Alexander Marynych, Matthias Meiners

Let $ξ_{1}, ξ_{2}, \dots$ be independent copies of a positive random variable $ξ$ , $S_{0} = 0$ , and $S_{k} = ξ_{1} + \dots + ξ_{k}$ , $k \in N$ . Define $N(t) = \inf\{k \in \mathbb{N}: S_…

math.PR2012

Exponential-Uniform Identities Related to Records

Alexander Gnedin, Alexander Marynych

We consider a rectangular grid induced by the south-west records from the planar Poisson point process in $R_{+}^{2}$ . A random symmetry property of the matrix whose entries are the ar…

math.PR2012

On asymptotics of the beta-coalescents

Alexander Gnedin, Alexander Iksanov, Alexander Marynych +1

We show that the total number of collisions in the exchangeable coalescent process driven by the beta $(1, b)$ measure converges in distribution to a 1-stable law, as the initial nu…