Complete convergence in mean for double arrays of random variables with values in Banach spaces

Son, Ta Cong, Thang, Dang Hung, and Dung, Le Van. "Complete convergence in mean for double arrays of random variables with values in Banach spaces." Applications of Mathematics 59.2 (2014): 177-190. <http://eudml.org/doc/261082>.

@article{Son2014,
abstract = {The rate of moment convergence of sample sums was investigated by Chow (1988) (in case of real-valued random variables). In 2006, Rosalsky et al. introduced and investigated this concept for case random variable with Banach-valued (called complete convergence in mean of order $p$). In this paper, we give some new results of complete convergence in mean of order $p$ and its applications to strong laws of large numbers for double arrays of random variables taking values in Banach spaces.},
author = {Son, Ta Cong, Thang, Dang Hung, Dung, Le Van},
journal = {Applications of Mathematics},
keywords = {complete convergence in mean; double array of random variables with values in Banach space; martingale difference double array; strong law of large numbers; $p$-uniformly smooth space; complete convergence in mean; double array of random variables with values in Banach space; martingale difference double array; strong law of large numbers; -uniformly smooth space},
language = {eng},
number = {2},
pages = {177-190},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Complete convergence in mean for double arrays of random variables with values in Banach spaces},
url = {http://eudml.org/doc/261082},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Son, Ta Cong
AU - Thang, Dang Hung
AU - Dung, Le Van
TI - Complete convergence in mean for double arrays of random variables with values in Banach spaces
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 177
EP - 190
AB - The rate of moment convergence of sample sums was investigated by Chow (1988) (in case of real-valued random variables). In 2006, Rosalsky et al. introduced and investigated this concept for case random variable with Banach-valued (called complete convergence in mean of order $p$). In this paper, we give some new results of complete convergence in mean of order $p$ and its applications to strong laws of large numbers for double arrays of random variables taking values in Banach spaces.
LA - eng
KW - complete convergence in mean; double array of random variables with values in Banach space; martingale difference double array; strong law of large numbers; $p$-uniformly smooth space; complete convergence in mean; double array of random variables with values in Banach space; martingale difference double array; strong law of large numbers; -uniformly smooth space
UR - http://eudml.org/doc/261082
ER -