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June 2016 Coupling on weighted branching trees
Ningyuan Chen, Mariana Olvera-Cravioto
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Adv. in Appl. Probab. 48(2): 499-524 (June 2016).

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.

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Ningyuan Chen. Mariana Olvera-Cravioto. "Coupling on weighted branching trees." Adv. in Appl. Probab. 48 (2) 499 - 524, June 2016.

Information

Published: June 2016
First available in Project Euclid: 9 June 2016

zbMATH: 1343.60127
MathSciNet: MR3511773

Subjects:
Primary: 60J80
Secondary: 60B10 , 60H25

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

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 2 • June 2016
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