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A note on the scaling limits of contour functions of Galton-Watson trees
HE Hui 1 * #,LUAN Na-Na 2
1.School of Mathematical Sciences, Beijing Normal University, Beijing 100875
2.School of Insurance, University of International Business and Economics, Beijing 100029
*Correspondence author
#Submitted by
Subject:
Funding: ***SRFDP （No.20110003120003）
Opened online:18 October 2013
Accepted by: none
Citation: HE Hui,LUAN Na-Na.A note on the scaling limits of contour functions of Galton-Watson trees[OL]. [18 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4562803
 
 
Recently, Abraham and Delmas constructed the distributions of super-critical L'evy trees truncated at a fixed height by connecting super-critical L'evy trees to (sub)critical L'evy trees via a martingale transformation. A similar relationship also holds for discrete Galton-Watson trees. In this paper, by the existing works on the convergence of contour functions of (sub)critical trees, the contour functions of truncated super-critical Galton-Watson trees are shown to converge weakly to the distributions constructed by Abraham and Delmas.
Keywords:Probability and Mathematical Statistics; Galton-Watson trees; Branching processes; L'evy trees; contour functions; scaling limit.
 
 
 

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