On convergence determining and separating classes of functions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Blount, Douglas²  Kouritzin, Michael A.¹ 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Arizona State Univ, Dept Math & Stat, Tempe, AZ 85287 USA

关键词: Probability measures;    Homeomorphism;    Weak convergence;    Skorokhod topology;    Lusin spaces;   

DOI  :  10.1016/j.spa.2010.05.018

来源: Elsevier

【 摘 要 】

Herein, we generalize and extend some standard results on the separation and convergence of probability measures. We use homeomorphism-based methods and work on incomplete metric spaces, Skorokhod spaces, Lusin spaces or general topological spaces. Our contributions are twofold: we dramatically simplify the proofs of several basic results in weak convergence theory and, concurrently, extend these results to apply more immediately in a number of settings, including on Lusin spaces. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free