Geodesic
Small deviation probabilities for sums of independent positive random variables, whose density has a~power decay at zero
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 195-203

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In the note small deviation probabilities of sum of i.i.d. positive random variables are studied, whose density has a power decay at zero. 
@article{ZNSL_2011_396_a12,
     author = {L. V. Rozovsky},
     title = {Small deviation probabilities for sums of independent positive random variables, whose density has a~power decay at zero},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {195--203},
     publisher = {mathdoc},
     volume = {396},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a12/}
}
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L. V. Rozovsky. Small deviation probabilities for sums of independent positive random variables, whose density has a~power decay at zero. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 195-203. http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a12/