### Coupling on weighted branching trees

#### Abstract

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

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

Dates
First available in Project Euclid: 9 June 2016

https://projecteuclid.org/euclid.aap/1465490760

Mathematical Reviews number (MathSciNet)
MR3511773

Zentralblatt MATH identifier
1343.60127

#### Citation

Chen, Ningyuan; Olvera-Cravioto, Mariana. Coupling on weighted branching trees. Adv. in Appl. Probab. 48 (2016), no. 2, 499--524. https://projecteuclid.org/euclid.aap/1465490760

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