Convergence to a Gaussian limit as the normalization exponent tends to 1/2

DOI10.1016/0167-7152(91)90191-SzbMath0729.60017OpenAlexW2055499859MaRDI QIDQ806155

Murad S. Taqqu, Norma Terrin

Publication date: 1991

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(91)90191-s

zbMATH Keywords

quadratic formlong-range dependenceself-similar processesasymptotic behavior of the quadratic formdouble Wiener-Itô integral

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic integrals (60H05) Self-similar stochastic processes (60G18)

Related Items (5)

Limit theorems for Toeplitz quadratic functionals of continuous-time stationary processes ⋮ The trace problem for Toeplitz matrices and operators and its impact in probability ⋮ Functional limit theorems for Toeplitz quadratic functionals of continuous time Gaussian stationary processes ⋮ Limit theorems for tapered Toeplitz quadratic functionals of continuous-time Gaussian stationary processes ⋮ Limit theorems for Toeplitz-type quadratic functionals of stationary processes and applications

Cites Work

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• A noncentral limit theorem for quadratic forms of Gaussian stationary sequences
• Central limit theorems for quadratic forms in random variables having long-range dependence
• Multiple Wiener-Ito integrals. With applications to limit theorems
• Convergence in distribution of sums of bivariate Appell polynomials with long-range dependence
• A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate
• Non-central limit theorems for non-linear functional of Gaussian fields

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