Maximal inequalities for multidimensionally indexed submartingale arrays
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.
scientific article; zbMATH DE number 4199170