Abstract:
In the note we study small deviation probabilities for sums of independent identically distributed positive random variables whose distribution function is slowly varying at zero.
Key words and phrases:
small deviations, sums of independent positive random variables, slowly varying functions.
Citation:
L. V. Rozovsky, “Small deviation probabilities for sums of independent positive random variables with distributions which are slowly varying at zero”, Probability and statistics. Part 19, Zap. Nauchn. Sem. POMI, 412, POMI, St. Petersburg, 2013, 237–251; J. Math. Sci. (N. Y.), 204:1 (2015), 155–164
\Bibitem{Roz13}
\by L.~V.~Rozovsky
\paper Small deviation probabilities for sums of independent positive random variables with distributions which are slowly varying at zero
\inbook Probability and statistics. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 412
\pages 237--251
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5653}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3073547}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 204
\issue 1
\pages 155--164
\crossref{https://doi.org/10.1007/s10958-014-2194-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925501295}
Linking options:
https://www.mathnet.ru/eng/znsl5653
https://www.mathnet.ru/eng/znsl/v412/p237
This publication is cited in the following 3 articles:
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”, Theory Probab. Appl., 63:1 (2018), 155–163
I. A. Ibragimov, M. A. Lifshits, A. I. Nazarov, D. N. Zaporozhets, “On the history of St. Petersburg school of probability and mathematical statistics: II. Random processes and dependent variables”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 213–236
L. V. Rozovsky, “Small deviation probabilities for sum of independent positive random variables, which have a common distribution, decreasing at zero not faster than a power”, J. Math. Sci. (N. Y.), 229:6 (2018), 767–771
Citation in format AMSBIB
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