Maximal inequalities for demimartingales and a strong law of large numbers
Ημερομηνία
2000Source
Statistics and Probability LettersVolume
50Issue
4Pages
357-363Google Scholar check
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Εμφάνιση πλήρους εγγραφήςΕπιτομή
Chow's maximal inequality for (sub)martingales is extended to the case of demi(sub)martingales introduced by Newman and Wright (Z. Wahrsch. Verw. Geb. 59 (1982) 361-371). This result serves as a "source" inequality for other inequalities such as the Hajek-Renyi inequality and Doob's maximal inequality and leads to a strong law of large numbers. The partial sum of mean zero associated random variables is a demimartingale. Therefore, maximal inequalities and a strong law of large numbers are obtained for associated random variables as special cases.