The universality of homogeneous polynomial forms and critical limits

DOI10.1007/s10959-015-0613-0zbMath1357.60021arXiv1505.03599OpenAlexW3098851543MaRDI QIDQ501838

Shuyang Bai, Murad S. Taqqu

Publication date: 10 January 2017

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.03599

zbMATH Keywords

weak convergencecentral limit theoremuniversalitylong memorylong-range dependenceWiener chaoshomogeneous polynomial forms

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05)

Related Items (2)

Fourth moment theorems on the Poisson space in any dimension ⋮ Limit theorems for long-memory flows on Wiener chaos

Cites Work

• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
• Central limit theorems for non-linear functionals of Gaussian fields
• Limit theorems for polylinear forms
• Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos
• Convergence of long-memory discrete \(k\)th order Volterra processes
• Generalized Hermite processes, discrete chaos and limit theorems
• Universal Gaussian fluctuations on the discrete Poisson chaos
• Normal Approximations with Malliavin Calculus
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
• The Invariance Principle for Stationary Processes
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