Stochastic fixed points for the maximum

Journal article, 2004

We consider stochastic fixed point equations X=sup_iT_iX_i (in distribution) in Xfor known $T=(T_1,T_2,... The rvs T,X_i,i = 1, 2, .. are independent and X_i distributed as X. We present a systematic approach in order to find solutions using the monotonicity of the corresponding operator. These equations come up in the natural setting of weighted trees with finite or countable many branches. Examples are in branching processes and the analysis of algorithms (for parallel computing).