Pruning a Lévy Continuum Random Tree
Pruning a Lévy Continuum Random Tree
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DOI：
10.1214/ejp.v15-802
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发表时间：
2008-04
影响因子：
1.4
通讯作者：
R. Abraham;Jean-François Delmas;G. Voisin
中科院分区：
文献类型：
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作者：
R. Abraham;Jean-François Delmas;G. Voisin
在给定一般临界或次临界分支机制的情况下，我们定义了相关的Levy连续体随机树的剪枝过程。这种修剪程序是通过在树上添加一些标记来定义的，使用了L的每条蛇技术。然后证明了剪枝后的子树仍然是L的一棵连续随机树。最后一个结果是用编码CRT的探索过程证明的，这是一种特殊的马尔可夫性和关于探索过程的鞅问题。最后给出了初始勘探过程和修剪过程的游程长度在游程度量下的联合规律。
Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated Levy continuum random tree. This pruning procedure is defined by adding some marks on the tree, using L'evy snake techniques. We then prove that the resulting sub-tree after pruning is still a L'evy continuum random tree. This last result is proved using the exploration process that codes the CRT, a special Markov property and martingale problems for exploration processes. We finally give the joint law under the excursion measure of the lengths of the excursions of the initial exploration process and the pruned one.