Invariance principle for stochastic processes with short memory

DOI10.1214/074921706000000734zbMath1122.60038arXivmath/0612707OpenAlexW1663008374MaRDI QIDQ3592305

Magda Peligrad, Sergey Utev

Publication date: 12 September 2007

Published in: High Dimensional Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612707

zbMATH Keywords

Brownian motioninvariance principlelinear processesstationary processweakly dependent sequencessample

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Generalizations of martingales (60G48) Special processes (60K99) Functional limit theorems; invariance principles (60F17)

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On the local limit theorems for psi-mixing Markov chains ⋮ On weak invariance principles for partial sums ⋮ Simultaneous confidence bands for sequential autoregressive fitting ⋮ On limit theorems for Banach-space-valued linear processes ⋮ Limit theorems in the context of multivariate long-range dependence ⋮ Asymptotic behavior of weakly dependent aggregated processes ⋮ Invariance principles for linear processes with application to isotonic regression ⋮ Functional central limit theorems for self-normalized partial sums of linear processes ⋮ Functional limit theorems for linear processes in the domain of attraction of stable laws ⋮ Asymptotic normality of sums of Hilbert space valued random elements ⋮ Limit Theorems for Aggregated Linear Processes ⋮ Asymptotic Properties for Linear Processes of Functionals of Reversible or Normal Markov Chains

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