A generalization of Strassen's functional LIL
Probability
2007-05-23 v2
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.
Cite
@article{arxiv.math/0601613,
title = {A generalization of Strassen's functional LIL},
author = {Uwe Einmahl},
journal= {arXiv preprint arXiv:math/0601613},
year = {2007}
}
Comments
16 pages