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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Some exponential moments of sums of independent random variables


Author: J. Kuelbs
Journal: Trans. Amer. Math. Soc. 240 (1978), 145-162
MSC: Primary 60B05; Secondary 60F15, 60G50
DOI: https://doi.org/10.1090/S0002-9947-1978-0517296-0
MathSciNet review: 0517296
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Abstract: If $\{ {X_n}\}$ is a sequence of vector valued random variables, $\{ {a_n}\}$ a sequence of positive constants, and $M = {\sup _{n \geqslant 1}}\left \| {({X_1} + \cdots + {X_n})/{a_n}} \right \|$, we examine when $E(\Phi (M)) < \infty$ under various conditions on $\Phi ,\{ {X_n}\}$, and $\{ {a_n}\}$. These integrability results easily apply to empirical distribution functions.


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Keywords: Multidimensional empirical distribution function, exponential inequalities, exponential moments of the supremum of partial sums
Article copyright: © Copyright 1978 American Mathematical Society