A strong approximation theorem for sums of random vectors in the domain of attraction to a stable law

DOI10.1007/BF01949061zbMath0615.60026OpenAlexW2009684721WikidataQ114852623 ScholiaQ114852623MaRDI QIDQ1820495

István Berkes, Walter Philipp, André Robert Dabrowski, Herold G. Dehling

Publication date: 1986

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01949061

zbMATH Keywords

invariance principleapproximation of partial sums

Mathematics Subject Classification ID

Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (6)

Strong approximation of the St. Petersburg game ⋮ On additive functionals of Markov chains ⋮ Almost sure and weak invariance principles for random variables attracted by a stable law ⋮ Scaling limits of directed polymers in spatial-correlated environment ⋮ Almost sure approximation of the superposition of the random processes ⋮ Testing for strict stationarity in a random coefficient autoregressive model

Cites Work

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• Weak and \(L^p\)-invariance principles for sums of \(B\)-valued random variables
• Approximation theorems for independent and weakly dependent random vectors
• An almost sure invariance principle for triangular arrays of banach space valued random variables
• Convergence of moments and related functional in the general central limit theorem in banach spaces
• A Note Concerning Behaviour of Iterated Logarithm Type
• A Limit Theoerm for Random Variables with Infinite Moments

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