Almost sure and weak invariance principles for random variables attracted by a stable law

DOI10.1007/BF00964369zbMath0661.60051OpenAlexW2030211536MaRDI QIDQ1113182

István Berkes, Herold G. Dehling

Publication date: 1989

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00964369

zbMATH Keywords

stable lawapproximation in probabiliysymmetric stable lawupper bound for the optimal remainder term

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Functional limit theorems; invariance principles (60F17)

Related Items (4)

Strong approximation of the St. Petersburg game ⋮ Strong Approximations for Partial Sums of Random Variables Attracted to a Stable Law ⋮ Strong approximation and a central limit theorem for St. Petersburg sums ⋮ Testing for strict stationarity in a random coefficient autoregressive model

Cites Work

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• A weak invariance principle with applications to domains of attraction
• An improvement of Strassen's invariance principle
• A strong approximation theorem for sums of random vectors in the domain of attraction to a stable law
• An almost sure invariance principle for random variables in the domain of attraction of a stable law
• Convergence of moments and related functional in the general central limit theorem in banach spaces
• On Large Deviation Problems for Sums of Random Variables which are not Attracted to the Normal Law
• Regularly varying functions

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