@article{MTMT:100861,
	title = {An approximation of partial sums of independent RV'-s, and the sample DF. I},
	url = {https://m2.mtmt.hu/api/publication/100861},
	author = {Komlós, János and Major, Péter and Tusnády, Gábor},
	doi = {10.1007/BF00533093},
	journal-iso = {Z WAHRSC VERW GEBIETE},
	journal = {ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE},
	volume = {32},
	unique-id = {100861},
	issn = {0044-3719},
	abstract = {Let Sn=X1+X2+⋯+Xnbe the sum of i.i.d.r.v.-s, EX1=0, EX12=1, and let Tn= Y1+Y2+⋯+Ynbe the sum of independent standard normal variables. Strassen proved in [14] that if X1 has a finite fourth moment, then there are appropriate versions of Snand Tn(which, of course, are far from being independent) such that |Sn -Tn|=O(n1/4(log n)1/1(log log n)1/4) with probability one. A theorem of Bártfai [1] indicates that even if X1 has a finite moment generating function, the best possible bound for any version of Sn, Tnis O(log n). In this paper we introduce a new construction for the pair Sn, Tn, and prove that if X1 has a finite moment generating function, and satisfies condition i) or ii) of Theorem 1, then |Sn -Tn|=O(log n) with probability one for the constructed Sn, Tn. Our method will be applicable for the approximation of sample DF., too. © 1975 Springer-Verlag.},
	year = {1975},
	pages = {111-131},
	orcid-numbers = {Major, Péter/0000-0003-1147-9523}
}