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arXiv · 1403.0397

A tree-valued Markov processes associated with an admissible family of branching mechanisms

Hongwei Bi·Hui He
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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 $\{{\mathcal T}_t\}$ by pruning L\'evy trees and an analogous process $\{{\mathcal T}^*_t\}$ 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 $\{{\mathcal T}_t\}$ at the ascension time can be represented by $\{{\mathcal T}^*_t\}$. The results generalize those studied in Abraham and Delmas (2012).

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Hongwei Bi, Hui He. 2014-03-03. A tree-valued Markov processes associated with an admissible family of branching mechanisms. https://arxiv.org/abs/1403.0397

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