TY  - JOUR
AU  - Berkes, István
AU  - Hörmann, S
AU  - Schauer, J
TI  - Asymptotic results for the empirical process of stationary sequences
JF  - STOCHASTIC PROCESSES AND THEIR APPLICATIONS
J2  - STOCH PROC APPL
VL  - 119
PY  - 2009
IS  - 4
SP  - 1298
EP  - 1324
PG  - 27
SN  - 0304-4149
DO  - 10.1016/j.spa.2008.06.010
UR  - https://m2.mtmt.hu/api/publication/169525
ID  - 169525
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Berkes, István
AU  - W, Philipp
TI  - An almost sure invariance principle for the empirical distribution function of mixing random variables
JF  - ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE
J2  - Z WAHRSC VERW GEBIETE
VL  - 41
PY  - 1977
IS  - 2
SP  - 115
EP  - 137
PG  - 23
SN  - 0044-3719
DO  - 10.1007/BF00538416
UR  - https://m2.mtmt.hu/api/publication/1781382
ID  - 1781382
N1  - WoS:hiba:A1977EG29000002 2019-03-02 23:54 első szerző nem egyezik, cím nem egyezik
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Komlós, János
AU  - Major, Péter
AU  - Tusnády, Gábor
TI  - An approximation of partial sums of independent RV'-s, and the sample DF. I
JF  - ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE
J2  - Z WAHRSC VERW GEBIETE
VL  - 32
PY  - 1975
IS  - 1-2
SP  - 111
EP  - 131
PG  - 21
SN  - 0044-3719
DO  - 10.1007/BF00533093
UR  - https://m2.mtmt.hu/api/publication/100861
ID  - 100861
AB  - 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.
LA  - English
DB  - MTMT
ER  -