Please use this identifier to cite or link to this item: https://doi.org/10.1214/10-AOP559
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dc.titleNew rates for exponential approximation and the theorems of Rényi and Yaglom
dc.contributor.authorPeköz, E.A.
dc.contributor.authorRöllin, A.
dc.date.accessioned2014-10-28T05:13:26Z
dc.date.available2014-10-28T05:13:26Z
dc.date.issued2011-03
dc.identifier.citationPeköz, 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
dc.identifier.issn00911798
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/105237
dc.description.abstractBoston 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.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1214/10-AOP559
dc.sourceScopus
dc.subjectCritical Galton-Watson branching process
dc.subjectEquilibrium and size-biased distribution
dc.subjectExponential approximation
dc.subjectFirst passage times
dc.subjectGeometric convolution
dc.subjectStein's method
dc.typeArticle
dc.contributor.departmentSTATISTICS & APPLIED PROBABILITY
dc.description.doi10.1214/10-AOP559
dc.description.sourcetitleAnnals of Probability
dc.description.volume39
dc.description.issue2
dc.description.page587-608
dc.identifier.isiut000288299600008
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