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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Some exponential moments of sums of independent random variables
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by J. Kuelbs PDF
Trans. Amer. Math. Soc. 240 (1978), 145-162 Request permission

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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Additional Information
  • © Copyright 1978 American Mathematical Society
  • 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