A survey of Max-type recursive distributional equations

• 成果类型: Article
• 署名作者: Aldous, DJ; Bandyopadhyay, A
• 署名单位: University of California System; University of California Berkeley; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000142
• 发表日期: 2005
• 页码: 1047-1110
• 关键词: fixed-points; limit; percolation; THEOREM; TREE

摘要

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-d = g((xi(i), X-i), i >= 1). Here (xi(i)) and g((.)) are given and the X-i 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 X-i, are the X-i measurable functions of the innovations process (xi(i))?