A generalization of Strassen's functional LIL

Uwe Einmahl

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A generalization of Strassen's functional LIL

Uwe Einmahl

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Abstract

Let X_1,X_2, . . . be a sequence of i.i.d. mean zero random variables and let S_n the sum of the first n random variables. We show that whenever lim sup_n |S_n|/c_n is finite with probability one and the normalizing sequence {c_n} is sufficiently regular, the corresponding normalized partial sum process sequence is relatively compact in C[0, 1] with canonical cluster set. Combining this result with some LIL type results in the infinite variance case, we obtain Strassen type results in this setting.

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Uwe Einmahl. 2006-08-25. A generalization of Strassen's functional LIL. https://arxiv.org/abs/math/0601613

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