On the Law of the Iterated Logarithm
Teicher, Henry
Ann. Probab., Tome 2 (1974) no. 6, p. 714-728 / Harvested from Project Euclid
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A triumvirate of sufficient conditions is given for unbounded, independent random variables to obey the Law of the Iterated Logarithm (LIL). As special cases, new results for weighted i.i.d. random variables and the Hartman-Wintner theorem are obtained. Necessity of finite variance for the two-sided LIL is shown to carry over for a large class of weighted i.i.d. random variables and the Marcinkiewicz-Zygmund example is generalized, simplified and clarified.
Publié le : 1974-08-14
Classification:  Two-Sided iterated logarithm law,  weighted i.i.d. random variables,  Marcinkiewicz-Zygmund growth,  Hartman condition,  60F15 
@article{1176996614,
     author = {Teicher, Henry},
     title = {On the Law of the Iterated Logarithm},
     journal = {Ann. Probab.},
     volume = {2},
     number = {6},
     year = {1974},
     pages = { 714-728},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996614}
}

Teicher, Henry. On the Law of the Iterated Logarithm. Ann. Probab., Tome 2 (1974) no. 6, pp.  714-728. http://gdmltest.u-ga.fr/item/1176996614/