An A.S. Invariance principle for lacunary seriesf(n k x)

DOI10.1007/BF01902603zbMath0429.60029OpenAlexW1981371622MaRDI QIDQ3866844

Walter Philipp, István Berkes

Publication date: 1979

Published in: Acta Mathematica Academiae Scientiarum Hungaricae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01902603

zbMATH Keywords

invariance principlelacunary series

Mathematics Subject Classification ID

Functional limit theorems; invariance principles (60F17)

Related Items (7)

On the class of limits of lacunary trigonometric series ⋮ Metric Discrepancy Results for Sequences {nkx} and Diophantine Equations ⋮ Diffusive behavior of ergodic sums over rotations ⋮ Irregular discrepancy behavior of lacunary series ⋮ On the law of the iterated logarithm for the discrepancy of lacunary sequences ⋮ On the asymptotic behavior of weakly lacunary series ⋮ On the law of the iterated logarithm for the discrepancy of lacunary sequences II

Cites Work

• The law of the iterated logarithm for a gap sequence with infinite gaps
• On the distribution of values of sums of the type \(\sum f(2^kt)\)
• Almost sure invariance principles for partial sums of weakly dependent random variables
• On the asymptotic behaviour of ?f(nkx)
• On the asymptotic behaviour of ?f(nkx)
• Probability methods in some problems of analysis and number theory
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