Email this article Local Limit Theorems for Densities in Orlicz Spaces
- Authors: Bobkov S.G.1
-
Affiliations:
- School of Mathematics, University of Minnesota
- Issue: Vol 242, No 1 (2019)
- Pages: 52-68
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/242950
- DOI: https://doi.org/10.1007/s10958-019-04466-9
- ID: 242950
Cite item
Open Access
Access granted
Subscription Access
Abstract
Necessary and sufficient conditions for the validity of the central limit theorem for densities are considered with respect to the norms in Orlicz spaces. The obtained characterization unites several results due to Gnedenko and Kolmogorov (uniform local limit theorem), Prokhorov (convergence in total variation) and Barron (entropic central limit theorem).
About the authors
S. G. Bobkov
School of Mathematics, University of Minnesota
Author for correspondence.
Email: bobko001@umn.edu
United States, Minneapolis, MN, 55455
Supplementary files
