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  - The functional law of the iterated logarithm for dependent random variables
JF  - ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE
J2  - Z WAHRSC VERW GEBIETE
VL  - 26
PY  - 1973
IS  - 3
SP  - 245
EP  - 258
PG  - 14
SN  - 0044-3719
DO  - 10.1007/BF00532727
UR  - https://m2.mtmt.hu/api/publication/2142580
ID  - 2142580
LA  - English
DB  - MTMT
ER  -