Abstract
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.
Citation
Tasos C. Christofides. Robert J. Serfling. "Maximal Inequalities for Multidimensionally Indexed Submartingale Arrays." Ann. Probab. 18 (2) 630 - 641, April, 1990. https://doi.org/10.1214/aop/1176990849
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