The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces

Nguyen Van Huan; Nguyen Van Quang

Kybernetika (2012)

  • Volume: 48, Issue: 2, page 254-267
  • ISSN: 0023-5954

Abstract

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We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.

How to cite

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Huan, Nguyen Van, and Quang, Nguyen Van. "The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces." Kybernetika 48.2 (2012): 254-267. <http://eudml.org/doc/247007>.

@article{Huan2012,
abstract = {We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.},
author = {Huan, Nguyen Van, Quang, Nguyen Van},
journal = {Kybernetika},
keywords = {the Doob inequality; strong law of large numbers; martingale difference array; Banach space; strong law of large numbers; the Doob inequality; martingale difference array; Banach space},
language = {eng},
number = {2},
pages = {254-267},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces},
url = {http://eudml.org/doc/247007},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Huan, Nguyen Van
AU - Quang, Nguyen Van
TI - The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 2
SP - 254
EP - 267
AB - We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
LA - eng
KW - the Doob inequality; strong law of large numbers; martingale difference array; Banach space; strong law of large numbers; the Doob inequality; martingale difference array; Banach space
UR - http://eudml.org/doc/247007
ER -

References

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