Lions, Pierre Louis; Toscani, Giuseppe A strengthened central limit theorem for smooth densities. (English) Zbl 0822.60018 J. Funct. Anal. 129, No. 1, 148-167 (1995). The paper presents various local limit theorems for i.i.d. random variables with zero mean and positive (but finite) variance. The authors employ two different setups. One is based on a generalization of Fisher’s information and the other uses Fourier transformation. The results give convergence in various norms depending on the properties of the theoretical density. Reviewer: P.Lachout (Praha) Cited in 13 Documents MSC: 60F05 Central limit and other weak theorems 62E20 Asymptotic distribution theory in statistics Keywords:local limit theorem; Fisher’s information; Fourier transformation; Sobolev spaces PDFBibTeX XMLCite \textit{P. L. Lions} and \textit{G. Toscani}, J. Funct. Anal. 129, No. 1, 148--167 (1995; Zbl 0822.60018) Full Text: DOI