Geodesic
On the functional law of the iterated logarithm for partially observed sums of random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 73-95 
N. L. Gorn; M. A. Lifshits. On the functional law of the iterated logarithm for partially observed sums of random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 73-95. http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a4/
@article{ZNSL_1997_244_a4,
     author = {N. L. Gorn and M. A. Lifshits},
     title = {On the functional law of the iterated logarithm for partially observed sums of random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {73--95},
     year = {1997},
     volume = {244},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a4/}
}
TY  - JOUR
AU  - N. L. Gorn
AU  - M. A. Lifshits
TI  - On the functional law of the iterated logarithm for partially observed sums of random variables
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1997
SP  - 73
EP  - 95
VL  - 244
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a4/
LA  - ru
ID  - ZNSL_1997_244_a4
ER  - 
%0 Journal Article
%A N. L. Gorn
%A M. A. Lifshits
%T On the functional law of the iterated logarithm for partially observed sums of random variables
%J Zapiski Nauchnykh Seminarov POMI
%D 1997
%P 73-95
%V 244
%U http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a4/
%G ru
%F ZNSL_1997_244_a4

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider partial-sum process generated by a sequence of nonidentically distributed independent random variables. Assuming that this process is available for observations along an arbitrary time sequence, we fill the gaps by linear interpolation and prove the functional law of the iterated logarithm (FLIL) for sample paths obtained in this way. Assuming that condition of V. A. Egorov holds, we show that FLIL is valid, while under other conditions sufficient for usual law of the iterated logarithm FLIL may fail.