On the asymptotic behaviour of ?f(nkx)

DOI10.1007/BF00535967zbMath0403.60004OpenAlexW127397713MaRDI QIDQ4188482

István Berkes

Publication date: 1976

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00535967

zbMATH Keywords

Wiener ProcessAsymptotic PropertiesMartingale Difference SequenceInvariance Principle For Martingales

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Brownian motion (60J65) Functional limit theorems; invariance principles (60F17)

Related Items (20)

On the central limit theorem for \(f(n_{k}x)\) ⋮ Random constructions for translates of non-negative functions ⋮ Almost everywhere convergence questions of series of translates of non-negative functions ⋮ Quantitative uniform distribution results for geometric progressions ⋮ Metric discrepancy results for subsequences of \(\{\theta^k x\}\) ⋮ On the central limit theorem for lacunary trigonometric series ⋮ GCD sums from Poisson integrals and systems of dilated functions ⋮ Effective Erdős-Wintner theorems for digital expansions ⋮ The law of the iterated logarithm for discrepancies of \(\{\theta^{n}x\}\) ⋮ The central limit theorem for Riesz-Raikov sums ⋮ An A.S. Invariance principle for lacunary seriesf(n k x) ⋮ On the law of the iterated logarithm for the discrepancy of lacunary sequences ⋮ On the pair correlations of powers of real numbers ⋮ The central limit theorem for complex Riesz-Raikov sums ⋮ Counterexamples in ergodic theory and number theory ⋮ LIMIT LAW FOR SOME MODIFIED ERGODIC SUMS ⋮ On the asymptotic behaviour of ?f(nkx) ⋮ The law of the iterated logarithm for the discrepancies of a permutation of \(\{n_kx\}\) ⋮ Convergence of series of dilated functions and spectral norms of GCD matrices ⋮ On the approximation of lacunary series by Brownian motion

Cites Work

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• On the distribution of values of the type \(\sum f(q^ k t)\)
• On certain systems of almost independent functions
• The law of the iterated logarithm for a gap sequence with infinite gaps
• The divergence of non-harmonic gap series
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Almost sure invariance principles for partial sums of weakly dependent random variables
• An invariance principle for the law of the iterated logarithm
• LACUNARY SERIES AND INDEPENDENT FUNCTIONS
• On the deviations in the Skorokhod-Strassen approximation scheme
• Limit theorems for lacunary series and uniform distribution mod 1
• An asymptotic property of a gap sequence
• A Gap Theorem
• Probability methods in some problems of analysis and number theory

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