Abstract:
Let {Xj} be i.i.d. positive random variables and let {λj} be a sequence of nonnegative nonincreasing numbers. We continue to examine the conditions under which asymptotics of the log Laplace transform of ∑j⩾1λjXj has an explicit form at infinity. A behavior of supj⩾1λjXj is also under consideration. Bibl. 14 titles.
Key words and phrases:
small deviations, positive random variables, slowly varying function, regularly varying function, Laplace transform.
Citation:
L. V. Rozovsky, “Small deviations of series of weighted positive random variables”, Probability and statistics. Part 16, Zap. Nauchn. Sem. POMI, 384, POMI, St. Petersburg, 2010, 212–224; J. Math. Sci. (N. Y.), 176:2 (2011), 224–231
\Bibitem{Roz10}
\by L.~V.~Rozovsky
\paper Small deviations of series of weighted positive random variables
\inbook Probability and statistics. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 384
\pages 212--224
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3892}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 176
\issue 2
\pages 224--231
\crossref{https://doi.org/10.1007/s10958-011-0413-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959539589}
Linking options:
https://www.mathnet.ru/eng/znsl3892
https://www.mathnet.ru/eng/znsl/v384/p212
This publication is cited in the following 7 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
Ibragimov I.A. Lifshits M.A. Nazarov A.I. Zaporozhets D.N., “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. Rozovskii, “Small deviation probabilities of weighted sum of independent random variables with a common distribution having a power decrease in zero under minimal moment assumptions”, Theory Probab. Appl., 62:3 (2018), 491–495
Rozovsky L.V., “Small deviation probabilities for weighted sum of independent random variables with a common distribution that can decrease at zero fast enough”, Stat. Probab. Lett., 117 (2016), 192–200
L. V. Rozovsky, “Small deviation probabilities for weighted sum of independent random variables with a common distribution, decreasing at zero not faster than a power”, J. Math. Sci. (N. Y.), 214:4 (2016), 540–545
Dobbs D., Melcher T., “Small Deviations For Time-Changed Brownian Motions and Applications To Second-Order Chaos”, Electron. J. Probab., 19 (2014), 85, 1–23
L. V. Rozovsky, “Small deviations of series of independent nonnegative random variables with smooth weights”, Theory Probab. Appl., 58:1 (2014), 121–137
Citation in format AMSBIB
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