Pruning Levy trees via an admissible family of branching mechanisms
Year: 2014
Type: preprint
Abstract: By studying an admissible family of branching mechanisms introduced in Li (2014), we obtain a pruning procedure on L\'evy trees. Then we could construct a decreasing L\'evy-CRT-valued process $\{\T_t\}$ by pruning L\'evy trees and an analogous process $\{\T^*_t\}$ by pruning a critical L\'evy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of $\{\T_t\}$ at the ascension time can be represented by $\{\T^*_t\}$. The results generalize those studied in Abraham and Delmas (2012).
Source: arXiv (Cornell University)
Author: Hui He
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2490376444