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A stochastic fixed point equation related to weighted branching with deterministic weights.

Alsmeyer, Gerold; Rösler, Uwe — 2006

Electronic Journal of Probability [electronic only]

A limit theorem for “quicksort”

Uwe Rösler — 1991

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

A stochastic fixed point equation for weighted minima and maxima

Gerold Alsmeyer; Uwe Rösler — 2008

Annales de l'I.H.P. Probabilités et statistiques

Given any finite or countable collection of real numbers , ∈, we find all solutions to the stochastic fixed point equation $W \overset{d}{=} inf_{j \in J} T_{j} W_{j},$ where and the , ∈, are independent real-valued random variables with distribution and $\overset{d}{=}$ means equality in distribution. The bulk of the necessary analysis is spent on the case when ||≥2 and all are (strictly) positive. Nontrivial solutions are then concentrated on either the positive or negative half line. In the most interesting...

The Martin entrance boundary of the Galton–Watson process

Gerold Alsmeyer; Uwe Rösler — 2006