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Asymptotic development for the CLT in total variation distance. (English) Zbl 1346.60016
Authors’ abstract: The aim of this paper is to study the asymptotic expansion in the total variation distance in the central limit theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an absolutely continuous component): we develop the error in powers of \(n^{-1/2}\) and give an explicit formula for the approximating measure.

MSC:
60F05 Central limit and other weak theorems
60H07 Stochastic calculus of variations and the Malliavin calculus
60H05 Stochastic integrals
60B10 Convergence of probability measures
60G50 Sums of independent random variables; random walks
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