## 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.## References

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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