2004/01/31 by David Aldous, David J. Aldous, Antar Bandyopadhyay · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #Probability and Statistical Research #math.PR #math.ST #msc:60E05 #msc:62E10 #msc:68Q25 #msc:82B44. #stat.TH
paper · pdf · doi:10.1214/105051605000000142
published as Annals of Applied Probability 2005, Vol. 15, No. 2, 1047-1110 · Published at http://dx.doi.org/10.1214/105051605000000142 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/05/01 · arxiv created 2005/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X\mathop=d g((ξi,Xi),i≥ 1). Here (ξi) and g(⋅) are given and the Xi are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g(⋅) is essentially a “maximum” or “minimum” function. We draw attention to the theoretical question of endogeny: in the associated recursive tree process Xi, are the Xi measurable functions of the innovations process (ξi)?