Invariance principles for logarithmic averages

DOI10.1017/S0305004100070870zbMath0766.60038OpenAlexW2084320447MaRDI QIDQ4034731

Miklós Csörgő, Lajos Horváth

Publication date: 16 May 1993

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100070870

zbMATH Keywords

almost sure central limit theoremOrnstein-Uhlenbeck processestwo-parameter processtwo-parameter Gaussian process

Mathematics Subject Classification ID

Functional limit theorems; invariance principles (60F17)

Related Items (19)

The law of large numbers with exceptional sets ⋮ On almost sure local and global central limit theorems ⋮ The logarithmic average of sample extremes is asymptotically normal. ⋮ A universal result in almost sure central limit theory. ⋮ On the logarithmic average of additive functionals ⋮ Between local and global logarithmic averages ⋮ Weight functions and pathwise local central limit theorems ⋮ Some distributional limit theorems for the maxima of Gaussian vector sequences ⋮ A strong approximation for logarithmic averages of partial sums of random variables ⋮ On the logarithmic average of iterated processes ⋮ Théorèmes limites avec poids pour les martingales vectorielles ⋮ On almost sure max-limit theorems ⋮ Non-asymptotic Gaussian estimates for the recursive approximation of the invariant distribution of a diffusion ⋮ On the random functional central limit theorems with almost sure convergence for subsequences ⋮ An extension of almost sure central limit theory ⋮ Refinement of the almost sure central limit theorem for associated processes ⋮ Almost sure central limit theorems for heavily trimmed sums ⋮ Logarithmic averages of stable random variables are asymptotically normal ⋮ Almost sure central limit theorems for m-dependent random variables

Cites Work

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• On higher-dimensional analogues of the arc-sine law
• On Strong Versions of the Central Limit Theorem
• An approximation of partial sums of independent RV's, and the sample DF. II
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Energy and the law of the interated logarithm.
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications

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