Some new maximal-type probability inequalities are developed for discrete-time multidimensionally indexed submartingales. In particular, the basic idea of Chow is abstracted and extended. This leads to a result which yields extended Kolmogorov inequalities and strong laws, extended Hajek-Renyi type inequalities competitive with Smythe and an extended Doob inequality which is counter-intuitive to a counterexample of Cairoli.
Publié le : 1990-04-14
Classification:
Multidimensionally indexed martingales,
maximal inequalities,
strong law of large numbers,
60G42,
60F15
@article{1176990849,
author = {Christofides, Tasos C. and Serfling, Robert J.},
title = {Maximal Inequalities for Multidimensionally Indexed Submartingale Arrays},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 630-641},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990849}
}
Christofides, Tasos C.; Serfling, Robert J. Maximal Inequalities for Multidimensionally Indexed Submartingale Arrays. Ann. Probab., Tome 18 (1990) no. 4, pp. 630-641. http://gdmltest.u-ga.fr/item/1176990849/