Maximal inequalities for multidimensionally indexed submartingale arrays. (English) Zbl 0726.60042

Some new maximal inequalities are proved for multi-parameter discrete submartingales. One of the ideas due to Y. S. Chow is extended and applied in the proofs of the results. A Hájek-Rényi-type inequality for a special case is obtained with a smaller constant. The classical Doob and Kolmogorov inequality and, moreover, the strong law of large numbers are generalized for the multi-parameter case.
Reviewer: F.Weisz (Budapest)


60G42 Martingales with discrete parameter
60F15 Strong limit theorems
Full Text: DOI