Coupling on weighted branching trees
Probability
2015-06-26 v4
Abstract
This paper considers linear functions constructed on two different weighted branching processes and provides 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.
Cite
@article{arxiv.1410.1050,
title = {Coupling on weighted branching trees},
author = {Ningyuan Chen and Mariana Olvera-Cravioto},
journal= {arXiv preprint arXiv:1410.1050},
year = {2015}
}