Geodesic
Small deviations of series of weighted positive random variables
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 212-224

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Let $\{X_j\}$ be i.i.d. positive random variables and let $\{\lambda_j\}$ be a sequence of nonnegative nonincreasing numbers. We continue to examine the conditions under which asymptotics of the log Laplace transform of $\sum_{j\ge1}\lambda_jX_j$ has an explicit form at infinity. A behavior of $\sup_{j\ge1}\lambda_jX_j$ is also under consideration. Bibl. 14 titles. 
@article{ZNSL_2010_384_a10,
     author = {L. V. Rozovsky},
     title = {Small deviations of series of weighted positive random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {212--224},
     publisher = {mathdoc},
     volume = {384},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a10/}
}
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L. V. Rozovsky. Small deviations of series of weighted positive random variables. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 212-224. http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a10/