The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin’s local time identity

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• 作者：David Aldous ; Grégory Miermont and Jim Pitman
• 关键词：Continuum random tree ; Exchangeable increments ; Exploration process ; L&eacute ; vy process ; Weak convergence
• 刊名：Probability Theory and Related Fields
• 出版年：2004
• 出版时间：June 2004
• 年：2004
• 卷：129
• 期：2
• 页码：182-218
• 全文大小：364 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Mathematical and Computational Physics
  Quantitative Finance
  Mathematical Biology
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064

文摘

We study the inhomogeneous continuum random trees (ICRT) that arise as weak limits of birthday trees. We give a description of the exploration process, a function defined on [0,1] that encodes the structure of an ICRT, and also of its width process, determining the size of layers in order of height. These processes turn out to be transformations of bridges with exchangeable increments, which have already appeared in other ICRT related topics such as stochastic additive coalescence. The results rely on two different constructions of birthday trees from processes with exchangeable increments, on weak convergence arguments, and on general theory on continuum random trees.