Maximal inequalities for multidimensionally indexed submartingale arrays (Q804084)
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scientific article; zbMATH DE number 4199170
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximal inequalities for multidimensionally indexed submartingale arrays |
scientific article; zbMATH DE number 4199170 |
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Maximal inequalities for multidimensionally indexed submartingale arrays (English)
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1990
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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.
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maximal inequalities
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multi-parameter discrete submartingales
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Hájek- Rényi-type inequality
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strong law of large numbers
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