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

作者：Bi, Hong Wei^*; He, Hui

来源：Acta Mathematica Sinica-English Series, 2019, 35(1): 135-160.

DOI：10.1007/s10114-018-8049-y

• Pruning
• admissible family
• branching process
• random tree
• Levy tree
• tree-valued process
• ascension process

Let (sic) subset of R be an interval. By studying an admissible family of branching mechanisms {psi(t), t is an element of (sic)} introduced in Li [Ann. Probab., 42, 41-79 (2014)], we construct a decreasing Levy-CRT-valued process {T-t, t is an element of (sic)} by pruning Levy trees accordingly such that for each t is an element of (sic), T-t is a psi(t)-Levy tree. We also obtain an analogous process {T-t*, t is an element of(sic)} 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 {T-t, t is an element of (sic)} at the ascension time A := inf{t is an element of (sic); T-t is finite} can be represented by {T-t*, t is an element of (sic)}. The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211 (2012)]. Keywords Pruning, admissible family, branching process, random tree, Levy tree, tree-valued process, ascension process

• 出版日期2019-1
• 单位对外经济贸易大学; 北京师范大学