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
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\Vert {({X_1} + \cdots + {X_n})/{a_n}} \right\Vert$, 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