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July 2001 Stein's Method and Birth-Death Processes
Timothy C. Brown, Aihua Xia
Ann. Probab. 29(3): 1373-1403 (July 2001). DOI: 10.1214/aop/1015345606


Barbour introduced a probabilistic view of Stein's method for estimating the error in probability approximations. However, in the case of approximations by general distributions on the integers, there have been no purely probabilistic proofs of Stein's bounds till this paper. Furthermore, the methods introduced here apply to a very large class of approximating distributions on the non-negative integers, among which there is a natural class for higher-order approximations by probability distributions rather than signed measures (as previously). The methods also produce Stein magic factors for process approximations which do not increase with the window of observation and which are simpler to apply than those in Brown, Weinberg and Xia.


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Timothy C. Brown. Aihua Xia. "Stein's Method and Birth-Death Processes." Ann. Probab. 29 (3) 1373 - 1403, July 2001.


Published: July 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1019.60019
MathSciNet: MR1872746
Digital Object Identifier: 10.1214/aop/1015345606

Primary: 60E05
Secondary: 60E15 , 60F05 , 60G55

Keywords: birth-death process , compound Poisson distribution , distributional approximation , negative binomial distribution , Poisson process approximation , polynomial birth-death distribution , Stein's method , total variation distance , Wasserstein distance

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 3 • July 2001
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