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A stochastic fixed point equation for weighted minima and maxima

Gerold AlsmeyerUwe 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 = d inf j J T j W j , where and the , ∈, are independent real-valued random variables with distribution and = 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...

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