Please use this identifier to cite or link to this item: https://doi.org/10.1214/10-AOP559
Title: New rates for exponential approximation and the theorems of Rényi and Yaglom
Authors: Peköz, E.A.
Röllin, A. 
Keywords: Critical Galton-Watson branching process
Equilibrium and size-biased distribution
Exponential approximation
First passage times
Geometric convolution
Stein's method
Issue Date: Mar-2011
Citation: Peköz, E.A., Röllin, A. (2011-03). New rates for exponential approximation and the theorems of Rényi and Yaglom. Annals of Probability 39 (2) : 587-608. ScholarBank@NUS Repository. https://doi.org/10.1214/10-AOP559
Abstract: Boston University and National University of Singapore We introduce two abstract theorems that reduce a variety of complex exponential distributional approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to theWasserstein and Kolmogorov metrics for the theorem of Rényi on random sums and generalizations of it, hitting times for Markov chains, and to obtain a new rate for the classical theorem of Yaglom on the exponential asymptotic behavior of a critical Galton-Watson process conditioned on nonextinction. The primary tools are an adaptation of Stein's method, Stein couplings, as well as the equilibrium distributional transformation from renewal theory. © Institute of Mathematical Statistics, 2011.
Source Title: Annals of Probability
URI: http://scholarbank.nus.edu.sg/handle/10635/105237
ISSN: 00911798
DOI: 10.1214/10-AOP559
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