@article{MTMT:2142559,
	title = {On the central limit theorem for f (nkx)},
	url = {https://m2.mtmt.hu/api/publication/2142559},
	author = {Aistleitner, C and Berkes, István},
	doi = {10.1007/s00440-008-0190-6},
	journal-iso = {PROBAB THEORY REL},
	journal = {PROBABILITY THEORY AND RELATED FIELDS},
	volume = {146},
	unique-id = {2142559},
	issn = {0178-8051},
	abstract = {By a classical observation in analysis, lacunary subsequences of the trigonometric system behave like independent random variables: they satisfy the central limit theorem, the law of the iterated logarithm and several related probability limit theorems. For subsequences of the system (f(nx))n≥1 with 2π-periodic fεL2 this phenomenon is generally not valid and the asymptotic behavior of (f(nkx))k≥1 is determined by a complicated interplay between the analytic properties of f (e.g., the behavior of its Fourier coefficients) and the number theoretic properties of nk. By the classical theory, the central limit theorem holds for f (nkx) if nk = 2k, or if nk+1/nk → α with a transcendental α, but it fails e.g., for nk = 2k - 1. The purpose of our paper is to give a necessary and sufficient condition for f (nkx) to satisfy the central limit theorem. We will also study the critical CLT behavior of f (nkx), i.e., the question what happens when the arithmetic condition of the central limit theorem is weakened "infinitesimally". © Springer-Verlag 2008.},
	keywords = {SEQUENCES; ASYMPTOTIC-BEHAVIOR; central limit theorem; TRIGONOMETRIC SERIES; Diophantine equations; Lacunary series; SIGMA-F(NKX); RIESZ-RAIKOV SUMS; NUMBER-THEORY},
	year = {2010},
	eissn = {1432-2064},
	pages = {267-289}
}

@article{MTMT:1926655,
	title = {An a.s. invariance principle for lacunary series f(nkx)},
	url = {https://m2.mtmt.hu/api/publication/1926655},
	author = {Berkes, István and W, Philipp},
	doi = {10.1007/BF01902603},
	journal-iso = {ACTA MATH ACAD SCI HUNG},
	journal = {ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE},
	volume = {34},
	unique-id = {1926655},
	issn = {0001-5954},
	year = {1979},
	pages = {141-155}
}

@article{MTMT:2142576,
	title = {On the asymptotic behaviour of {perspective}f(nkx) - Applications},
	url = {https://m2.mtmt.hu/api/publication/2142576},
	author = {Berkes, István},
	doi = {10.1007/BF00535968},
	journal-iso = {Z WAHRSC VERW GEBIETE},
	journal = {ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE},
	volume = {34},
	unique-id = {2142576},
	issn = {0044-3719},
	year = {1976},
	pages = {347-365}
}

@article{MTMT:2142577,
	title = {On the asymptotic behaviour of {perspective}f(nkx) - Main theorems},
	url = {https://m2.mtmt.hu/api/publication/2142577},
	author = {Berkes, István},
	doi = {10.1007/BF00535967},
	journal-iso = {Z WAHRSC VERW GEBIETE},
	journal = {ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE},
	volume = {34},
	unique-id = {2142577},
	issn = {0044-3719},
	year = {1976},
	pages = {319-345}
}