Journal of Theoretical Probability

, Volume 22, Issue 1, pp 82–98 | Cite as

On Asymptotic Proximity of Distributions

Article

Abstract

We consider some general facts concerning the convergence
$$P_{n}-Q_{n}\rightarrow0\quad\mbox{as}\ n\rightarrow\infty,$$
where P n and Q n are probability measures in a complete separable metric space. The main point is that the sequences {P n } and {Q n } are not assumed to be tight. We compare different possible definitions of the above convergence and establish some general properties.

Keywords

Proximity of distributions Merging of distributions Weak convergence The central asymptotic problem Asymptotic proximity of distributions 

Mathematics Subject Classification (2000)

60F17 60G15 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Laboratoire Paul Painlevé–UMR 8524Université de Lille I–Bat. M2Villeneuve d’AscqFrance
  2. 2.Department of Mathematics and StatisticsSan Diego State UniversitySan DiegoUSA
  3. 3.Central Economics and Mathematics InstituteRussian Academy of SciencesMoscowRussia

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