Fabian Buckmann

most citedStability of perpetuities in Markovian environment

5 citations · 5 across the 1 of their papers we have counts for

collaborators

3 papers

math.PR2017

An Arcsine Law for Markov Random Walks

Gerold Alsmeyer, Fabian Buckmann

The classic arcsine law for the number $N_{n}^{>} := n^{- 1} \sum_{k = 1}^{n} 1_{{S_{k} > 0}}$ of positive terms, as $n \to \infty$ , in an ordinary random walk $(S_{n})_{n \geq 0}$ i…

math.PR2016★ 5 cited

Stability of perpetuities in Markovian environment

Gerold Alsmeyer, Fabian Buckmann

The stability of iterations of affine linear maps $Ψ_{n} (x) = A_{n} x + B_{n}$ , $n = 1, 2, \dots$ , is studied in the presence of a Markovian environment, more precisely, for the situation…

math.PR2016

Fluctuation theory for Markov random walks

Gerold Alsmeyer, Fabian Buckmann

Two fundamental theorems by Spitzer/Erickson and Kesten/Maller on the fluctuation type (positive divergence, negative divergence or oscillation) of a real-valued random walk $(S_{n…