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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
By studying an admissible family of branching mechanisms introduced in Li (2014), a pruning procedure on L'evy trees is obtained. Then a decreasing L'evy-CRT-valued process ${T_t}$ by pruning L'evy trees and an analogous process ${T^*_t}$ are constructed by pruning a critical L'evy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, it is shown 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).
Keywords:Probability and Mathematical Statistics;admissible family of branching mechanisms; Branching processes; L'evy trees; pruning