Characteristic Functions, Moments, and the Central Limit Theorem

DOI10.1214/aoms/1177697109zbMath0196.21204OpenAlexW2035468159MaRDI QIDQ5592741

Bruce M. Brown

Publication date: 1970

Published in: The Annals of Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoms/1177697109

zbMATH Keywords

probability theory

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10)

Related Items (19)

Fractional absolute moments of heavy tailed distributions ⋮ Distribution and moment convergence of martingales ⋮ Uniform integrability of the OLS estimators, and the convergence of their moments ⋮ Formulae for absolute moments ⋮ Characteristic function of the positive part of a random variable and related results, with applications ⋮ Extreme order statistics of random walks ⋮ The expected $L_{p}$ norm of random polynomials ⋮ On the accuracy of the approximation of the complex exponent by the first terms of its Taylor expansion with applications ⋮ Positive-part moments via characteristic functions, and more general expressions ⋮ Central limit theorem by moments ⋮ Positive-part moments via the Fourier-Laplace transform ⋮ The convergence of moments in the martingale central limit theorem ⋮ On the L^p convergence of sums of independent random variables ⋮ Formulas of absolute moments ⋮ On the duality between the behaviour of sums of independent random variables and the sums of their squares ⋮ On decoupling in Banach spaces ⋮ Moment bounds for stationary mixing sequences ⋮ The convergence of moments in the central limit theorem for stationary phi-mixing processes ⋮ On the \(L_ p\) norm for some approximation operators

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