Local Limit Theorems for Densities in Orlicz Spaces

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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 languageEnglish (US)
Pages (from-to)52-68
Number of pages17
JournalJournal of Mathematical Sciences (United States)
Issue number1
StatePublished - Oct 7 2019


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