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Teoriya Veroyatnostei i ee Primeneniya, 2018, Volume 63, Issue 1, Pages 191–202
DOI: https://doi.org/10.4213/tvp5157 (Mi tvp5157) 		 
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
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DOI: https://doi.org/10.4213/tvp5157
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.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00367
This work was supported by the Russian Foundation for Basic Research (grant 16-01-00367).
Received: 29.05.2016
Revised: 30.08.2017
Accepted: 20.10.2017
English version:
Theory of Probability and its Applications, 2018, Volume 63, Issue 1, Pages 155–163
DOI: https://doi.org/10.1137/S0040585X97T988976
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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