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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some one-sided theorems on the tail distribution of sample sums with applications to the last time and largest excess of boundary crossings


Authors: Y. S. Chow and T. L. Lai
Journal: Trans. Amer. Math. Soc. 208 (1975), 51-72
MSC: Primary 60G50
MathSciNet review: 0380973
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Abstract: In this paper, we prove certain one-sided Paley-type inequalities and use them to study the convergence rates for the tail probabilities of sample sums. We then apply our results to find the limiting moments and the limiting distribution of the last time and the largest excess of boundary crossings for the sample sums, generalizing the results previously obtained by Robbins, Siegmund and Wendel. Certain one-sided limit theorems for delayed sums are also obtained and are applied to study the convergence rates of tail probabilities.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0380973-6
PII: S 0002-9947(1975)0380973-6
Keywords: Convergence rates, Paley-type inequalities, last time, largest excess, limiting distribution, limiting moments, delayed sums
Article copyright: © Copyright 1975 American Mathematical Society