Advances in Applied Probability

Coupling on weighted branching trees

Ningyuan Chen and Mariana Olvera-Cravioto

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In this paper we consider linear functions constructed on two different weighted branching processes and provide explicit bounds for their Kantorovich–Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector has a different dependence structure from the usual one. By applying the bounds to sequences of weighted branching processes, we derive sufficient conditions for the convergence in the Kantorovich–Rubinstein distance of linear functions. We focus on the case where the limits are endogenous fixed points of suitable smoothing transformations.

Article information

Adv. in Appl. Probab., Volume 48, Number 2 (2016), 499-524.

First available in Project Euclid: 9 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60B10: Convergence of probability measures 60H25: Random operators and equations [See also 47B80]

Weighted branching processes smoothing transform coupling Kantorovich–Rubinstein distance Wasserstein distance weak convergence


Chen, Ningyuan; Olvera-Cravioto, Mariana. Coupling on weighted branching trees. Adv. in Appl. Probab. 48 (2016), no. 2, 499--524.

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