On Asymptotic Proximity of Distributions

2007/05/18 by Youri Davydov, Davydov Youri, Youri, Davydov +3
Mathematics · #60F17 #60G15 #60G15 60F17 #FOS: Mathematics #Mathematical and Theoretical Analysis #Probability (math.PR) #math.PR #msc:60F17 #msc:60G15

paper · pdf · doi:10.48550/arxiv.0705.2677

21 pages, added reference, adapted content, corrected typos

openalex publication_date 2007/05/18 · arxiv created 2007/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider some general facts concerning convergence P_n-Q_n→ 0 as n→ ∞, 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.

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