A Tree-valued Markov Process Associated with an Admissible Family of Branching Mechanisms  

作　　者：Hong Wei BI Hui HE 

机构地区：[1]School of Insurance and Economics,University of International Business and Economics,Beijing 100029.P.R.China [2]Laboratory of Mathematics and Complex Systems,School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2019年第1期135-160,共26页数学学报（英文版）

基　　金：supported by NSFC(Grant No.11801075);supported by NSFC(Grant Nos.11671041,11531001 and 11371061);the Fundamental Research Funds for the Central Universities in UIBE(Grant No.16QN04)

摘　　要：Let E■R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].Let E?R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].

关 键 词：Pruning admissible family branching process random tree Lévy tree tree-valued process ascension process 

分 类 号：O1[理学—数学]