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On Distributional Properties of Perpetuities

- G. Alsmeyer, A. Iksanov, U. Rösler
- Mathematics
- 26 March 2008

We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate,… Expand

Rate of convergence in the law of large numbers for supercritical general multi-type branching processes

- A. Iksanov, M. Meiners
- Mathematics
- 7 January 2014

Renewal Theory for Perturbed Random Walks and Similar Processes

- A. Iksanov
- Mathematics
- 11 December 2016

Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent

- M. Drmota, A. Iksanov, M. Moehle, U. Roesler
- Mathematics
- 1 October 2007

The Bernoulli sieve: an overview

- A. Gnedin, A. Iksanov, A. Marynych
- Mathematics
- 31 May 2010

The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative random walk, also known as the… Expand

Functional limit theorems for divergent perpetuities in the contractive case

- D. Buraczewski, A. Iksanov
- Mathematics
- 9 November 2014

Let $\big(M_k, Q_k\big)_{k\in\mathbb{N}}$ be independent copies of an $\mathbb{R}^2$-valued random vector. It is known that if $Y_n:=Q_1+M_1Q_2+...+M_1\cdot...\cdot M_{n-1}Q_n$ converges a.s. to a… Expand

A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree

- M. Drmota, A. Iksanov, M. Moehle, U. Roesler
- Mathematics, Computer ScienceRandom Struct. Algorithms
- 1 May 2009

TLDR

On the number of jumps of random walks with a barrier

- A. Iksanov, M. Möhle
- MathematicsAdvances in Applied Probability
- 1 March 2008

Let S 0 := 0 and Sk := ξ 1 + ··· + ξk for k ∈ ℕ := {1, 2, …}, where {ξk : k ∈ ℕ} are independent copies of a random variable ξ with values in ℕ and distribution pk := P{ξ = k}, k ∈ ℕ. We interpret… Expand

On Λ-Coalescents with Dust Component

- A. Gnedin, A. Iksanov, A. Marynych
- Mathematics, PhysicsJournal of Applied Probability
- 1 December 2011

We consider the Λ-coalescent processes with a positive frequency of singleton clusters. The class in focus covers, for instance, the beta(a, b)-coalescents with a > 1. We show that some large-sample… Expand

Small parts in the Bernoulli sieve

- A. Gnedin, A. Iksanov, U. Roesler
- Mathematics
- 18 April 2008

Sampling from a random discrete distribution induced by a 'stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and… Expand

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