On the functional law of the iterated logarithm for partially observed sums of random variables
The authors consider partial-sum processes generated by a sequence of non-identically distributed random variables. If this process is available for observation only along a subsequence of time epochs, the gaps are filled by linear interpolation. For the sample paths obtained in this way a functional law of iterated logarithm (FLIL) is proved under the assumption that the Egorov condition holds. Furthermore, it is pointed out that other conditions (like the Petrov or the Kolmogorov condition) implying the usual law of iterated logarithm are in general not sufficient to hold the FLIL.
functional law of the iterated logarithm
scientific article; zbMATH DE number 1495312