Geodesic
Small deviations of the maximal element of a sequence of independent variables with smooth weights
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 190-200 
L. V. Rozovsky. Small deviations of the maximal element of a sequence of independent variables with smooth weights. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 190-200. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a14/
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     author = {L. V. Rozovsky},
     title = {Small deviations of the maximal element of a~sequence of independent variables with smooth weights},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {190--200},
     year = {2009},
     volume = {368},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a14/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We study the logarithmic small deviations of the maximal element of a sequence $\{\lambda_jX_j\}$, where $\{X_j\}$ are independent copies of non-negative random variable $X$ and $\{\lambda_j\}$ is a non-increasing sequence of positive numbers, satisfying certain conditions of regularity. Bibl. – 3 titles.

[1] F. Aurzada, “On the lower tail probabilities of some random sequences in $l_p$”, J. Theoret. Probab., 20 (2007), 843–858 | DOI | MR | Zbl

[2] F. Aurzada, “A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights”, Statist. Probab. Lett., 78 (2008), 2300–2307 | DOI | MR | Zbl

[3] L. V. Rozovsky, “Small deviations of series of weighted i.i.d. non-negative random variables with a positive mass at the origin”, Statist. Probab. Lett., 79 (2009), 1495–1500 | DOI | MR | Zbl