Some exponential moments of sums of independent random variables

Kuelbs, J.

doi:10.1090/S0002-9947-1978-0517296-0

Some exponential moments of sums of independent random variables
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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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