Equivalent conditions on the central limit theorem for a sequence of probability measures on R

✍ Scribed by Toshio Mikami

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 217 KB
• Volume: 37
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(97)00122-3

✦ Synopsis

In this paper we give equivalent conditions on the central limit theorem in total variation norm for a sequence of probability measures on ~. This generalizes Cacoullos, Papathanasiou and Utev's central limit theorem in Lt-norm for a sequence of probability density functions on R. We also give equivalent conditions on the central limit theorem in weak convergence and those on the local limit theorem.