Local Limit Theorems for Densities in Orlicz Spaces

S. G. Bobkov

doi:10.1007/s10958-019-04466-9

Local Limit Theorems for Densities in Orlicz Spaces

S. G. Bobkov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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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).

Original language	English (US)
Pages (from-to)	52-68
Number of pages	17
Journal	Journal of Mathematical Sciences (United States)
Volume	242
Issue number	1
DOIs	https://doi.org/10.1007/s10958-019-04466-9
State	Published - Oct 7 2019

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© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

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Local Limit Theorems for Densities in Orlicz Spaces

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