@article{MTMT:1923467,
	title = {Approximation theorems for independent and weakly dependent random vectors},
	url = {https://m2.mtmt.hu/api/publication/1923467},
	author = {Berkes, István and Philipp, W},
	doi = {10.1214/aop/1176995146},
	journal-iso = {ANN PROBAB},
	journal = {ANNALS OF PROBABILITY},
	volume = {7},
	unique-id = {1923467},
	issn = {0091-1798},
	abstract = {In this paper we prove approximation theorems of the following type. Let {Xk,k⩾1} be a sequence of random variables with values in Rdk,dk⩾1 and let {Gk,k⩾1} be a sequence of probability distributions on Rdk with characteristic functions gk respectively. If for each k⩾1 the conditional characteristic function of Xk given X1,⋯,Xk−1 is close to gk and if Gk has small tails, then there exists a sequence of independent random variables Yk with distribution Gk such that |Xk−Yk| is small with large probability. As an application we prove almost sure invariance principles for sums of independent identically distributed random variables with values in Rd and for sums of ϕ-mixing random variables with a logarithmic mixing rate.},
	year = {1979},
	eissn = {2168-894X},
	pages = {29-54}
}

@article{MTMT:2142580,
	title = {The functional law of the iterated logarithm for dependent random variables},
	url = {https://m2.mtmt.hu/api/publication/2142580},
	author = {Berkes, István},
	doi = {10.1007/BF00532727},
	journal-iso = {Z WAHRSC VERW GEBIETE},
	journal = {ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE},
	volume = {26},
	unique-id = {2142580},
	issn = {0044-3719},
	year = {1973},
	pages = {245-258}
}