TY  - JOUR
AU  - Berkes, István
TI  - A central limit theorem for trigonometric series with small gaps
JF  - ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE
J2  - Z WAHRSC VERW GEBIETE
VL  - 47
PY  - 1979
SP  - 157
EP  - 161
PG  - 5
SN  - 0044-3719
DO  - 10.1007/BF00535280
UR  - https://m2.mtmt.hu/api/publication/1926686
ID  - 1926686
N1  - WoS:hiba:A1979GM12300003 2019-03-03 01:42 cím nem egyezik
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Berkes, István
AU  - Philipp, W
TI  - Approximation theorems for independent and weakly dependent random vectors
JF  - ANNALS OF PROBABILITY
J2  - ANN PROBAB
VL  - 7
PY  - 1979
IS  - 1
SP  - 29
EP  - 54
PG  - 26
SN  - 0091-1798
DO  - 10.1214/aop/1176995146
UR  - https://m2.mtmt.hu/api/publication/1923467
ID  - 1923467
AB  - 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.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Berkes, István
TI  - On a central limit theorem for lacunary trigonometric series
JF  - ANALYSIS MATHEMATICA
J2  - ANAL MATH
VL  - 4
PY  - 1978
SP  - 159
EP  - 180
PG  - 22
SN  - 0133-3852
DO  - 10.1007/BF01908987
UR  - https://m2.mtmt.hu/api/publication/1926682
ID  - 1926682
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  - Berkes, István
TI  - An almost sure invariance principle for lacunary trigonometric series
JF  - ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE
J2  - ACTA MATH ACAD SCI HUNG
VL  - 26
PY  - 1975
IS  - 1-2
SP  - 209
EP  - 220
PG  - 12
SN  - 0001-5954
DO  - 10.1007/BF01895964
UR  - https://m2.mtmt.hu/api/publication/2142578
ID  - 2142578
N1  - WoS:hiba:A1975AA06700022 2019-03-08 03:53 cím nem egyezik
LA  - English
DB  - MTMT
ER  -