Geodesic
Small deviation probabilities for weighted sum of independent random variables with a common distribution, decreasing at zero not faster than a power
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 178-185 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the note we give estimates of small deviation probabilities of a sum $\sum_{j\ge1}\lambda_jX_j$, where $\{\lambda_j\}$ are positive numbers and $\{X_j\}$ are i.i.d. positive random variables, satisfying mild assumptions at zero and infinity. 
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L. V. Rozovsky. Small deviation probabilities for weighted sum of independent random variables with a common distribution, decreasing at zero not faster than a power. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 178-185. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a10/

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