A Stochastic Fixed Point Equation Related to Weighted Branching with Deterministic Weights

A stochastic fixed point equation for weighted minima and maxima

Given any finite or countable collection of real numbers Tj , j ∈ J , we find all solutions F to the stochastic fixed point equation W d = inf j∈J TjWj , where W and the Wj , j ∈ J , are independent real-valued random variables with distribution F and d = means equality in distribution. The bulk of the necessary analysis is spent on the case when |J | ≥ 2 and all Tj are (strictly) positive. Non...

The Weighted Branching Process and Its Associated Stochastic Fixed Point Equation

A Min-Type Stochastic Fixed-Point Equation Related to the Smoothing Transformation

This paper is devoted to the study of the stochastic fixed-point equation X d = inf i≥1:Ti>0 Xi/Ti and the connection with its additive counterpart X d = ∑ i≥1 TiXi associated with the smoothing transformation. Here d = means equality in distribution, T def = (Ti)i≥1 is a given sequence of nonnegative random variables and X,X1, . . . is a sequence of nonnegative i.i.d. random variables independ...

A Stochastic Maximin Fixed-point Equation Related to Game Tree Evaluation

After suitable normalization the asymptotic root value W of a minimax game tree of order b ≥ 2 with independent and identically distributed input values having a continuous, strictly increasing distribution function on a subinterval ofR appears to be a particular solution of the stochastic maximin fixed-point equation W L = ξ max1≤i≤b min1≤j≤b Wi,j , where Wi,j are independent copies of W and L...

Random fixed point theorems with an application to a random nonlinear integral equation

In this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. We discuss also the existence of a solution to a nonlinear random integral equation in Banah spaces.