Some exponential moments of sums of independent random variables-Reference-Cited by-同舟云学术

Some exponential moments of sums of independent random variables

Published:1978 Issue:0 Volume:240 Page:145-162
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Kuelbs J.

Abstract

If { X n } \{ {X_n}\} is a sequence of vector valued random variables, { a n } \{ {a_n}\} a sequence of positive constants, and M = sup n ⩾ 1 ‖ ( X 1 + ⋯ + X n ) / a n ‖ M = {\sup _{n \geqslant 1}}\left \| {({X_1} + \cdots + {X_n})/{a_n}} \right \| , we examine when E ( Φ ( M ) ) > ∞ E(\Phi (M)) > \infty under various conditions on Φ , { X n } \Phi ,\{ {X_n}\} , and { a n } \{ {a_n}\} . These integrability results easily apply to empirical distribution functions.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1978-240-00/S0002-9947-1978-0517296-0/S0002-9947-1978-0517296-0.pdf

Reference18 articles.

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3. The law of the iterated logarithm for empirical distributions;Finkelstein, Helen;Ann. Math. Statist.,1971

4. Central limit theorem in a Banach space;Jain, Naresh C.,1976

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