NEW RATES FOR EXPONENTIAL APPROXIMATION AND THE THEOREMS OF RENYI AND YAGLOM

• 成果类型: Article
• 署名作者: Pekoez, Erol A.; Roellin, Adrian
• 署名单位: Boston University; National University of Singapore
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP559
• 发表日期: 2011
• 页码: 587-608
• 关键词: steins method; bounds; inequalities; zero

摘要

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 the Wasserstein and Kolmogorov metrics for the theorem of Renyi 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.