On limit theorems for Banach-space-valued linear processes

DOI10.1007/s10986-010-9072-6zbMath1207.60028OpenAlexW1997902087MaRDI QIDQ619353

Charles Suquet, Alfredas Račkauskas

Publication date: 24 January 2011

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-010-9072-6

zbMATH Keywords

functional central limit theoremlinear processHölder spacecentral limit theorem in Banach spacespartialsum process

Mathematics Subject Classification ID

Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

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Cites Work

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• Testing epidemic changes of infinite dimensional parameters
• Recent advances in invariance principles for stationary sequences
• Asymptotics for linear processes
• Sharp conditions for the CLT of linear processes in a Hilbert space
• Linear processes in function spaces. Theory and applications
• Necessary and sufficient condition for the functional central limit theorem in Hölder spaces
• Hölder norm test statistics for epidemic change
• The invariance principle for Banach space valued random variables
• The conditional central limit theorem in Hilbert spaces.
• Invariance principle for stochastic processes with short memory
• Hölderian invariance principle for Hilbertian linear processes

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