Asymptotic development for the CLT in total variation distance
Copyright policy )Asymptotic development for the CLT in total variation distance
The aim of this paper is to study the asymptotic expansion in total variation 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.
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], total variation distance, Abstract Malliavin calculus; integration by parts; regularizing functions; total variation distance., Sums of independent random variables; random walks, Stochastic calculus of variations and the Malliavin calculus, Stochastic integrals, Probability (math.PR), central limit theorem, Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA, Central limit and other weak theorems, integration by part, regularizing functions, abstract Malliavin calculus, regularizing function, Abstract Malliavin calculu, 60F05, 60H07, 60F05, integration by parts, FOS: Mathematics, Convergence of probability measures, Mathematics - Probability, regularizing functions 2000 MSC: 60H07
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], total variation distance, Abstract Malliavin calculus; integration by parts; regularizing functions; total variation distance., Sums of independent random variables; random walks, Stochastic calculus of variations and the Malliavin calculus, Stochastic integrals, Probability (math.PR), central limit theorem, Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA, Central limit and other weak theorems, integration by part, regularizing functions, abstract Malliavin calculus, regularizing function, Abstract Malliavin calculu, 60F05, 60H07, 60F05, integration by parts, FOS: Mathematics, Convergence of probability measures, Mathematics - Probability, regularizing functions 2000 MSC: 60H07
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