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Short Communications
Small deviation probabilities for a weighted sum of independent positive random variables with common distribution function that can decrease at zero fast enough
L. V. Rozovskii Saint-Petersburg Chemical-Pharmaceutical Academy
Abstract:
The present note puts forward the most general conditions to date under
which the classical asymptotics of the small deviation probabilities
for a weighted sum of independent positive random
variables takes place. Regarding random variables it is assumed that their common distribution function
can, in particular, have an exponential falloff at zero.
Keywords:
small deviations, sums of independent positive random variables.
Received: 29.05.2016 Revised: 30.08.2017 Accepted: 20.10.2017
Citation:
L. V. Rozovskii, “Small deviation probabilities for a weighted sum of independent positive random variables with common distribution function that can decrease at zero fast enough”, Teor. Veroyatnost. i Primenen., 63:1 (2018), 191–202; Theory Probab. Appl., 63:1 (2018), 155–163
Linking options:
https://www.mathnet.ru/eng/tvp5157https://doi.org/10.4213/tvp5157 https://www.mathnet.ru/eng/tvp/v63/i1/p191
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