Abstract:
In the note we give estimates of small deviation probabilities of a sum ∑j⩾1λjXj, where {λj} are nonnegative numbers and {Xj} are i.i.d. positive random variables, satisfying mild assumptions at zero and infinity.
Citation:
L. V. Rozovskii, “Small deviation probabilities for sums of independent positive random variables”, Probability and statistics. Part 11, Zap. Nauchn. Sem. POMI, 341, POMI, St. Petersburg, 2007, 151–167; J. Math. Sci. (N. Y.), 147:4 (2007), 6935–6945
\Bibitem{Roz07}
\by L.~V.~Rozovskii
\paper Small deviation probabilities for sums of independent positive random variables
\inbook Probability and statistics. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 341
\pages 151--167
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl141}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2363592}
\zmath{https://zbmath.org/?q=an:1137.60013}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 147
\issue 4
\pages 6935--6945
\crossref{https://doi.org/10.1007/s10958-007-0518-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36048937308}
Linking options:
https://www.mathnet.ru/eng/znsl141
https://www.mathnet.ru/eng/znsl/v341/p151
This publication is cited in the following 14 articles:
Leonid Rozovsky, “On Small Deviation Asymptotics in the L2-Norm for Certain Gaussian Processes”, Mathematics, 9:6 (2021), 655
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 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
L. V. Rozovskii, “Small deviation probabilities of weighted sums of independent positive random variables with a common distribution that decreases at zero not faster than a power”, Theory Probab. Appl., 60:1 (2016), 142–150
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
Daniel Dobbs, Tai Melcher, “Small deviations for time-changed Brownian motions and applications to second-order chaos”, Electron. J. Probab., 19:none (2014)
L.V. Rozovsky, “Small deviation probabilities of weighted sums under minimal moment assumptions”, Statistics & Probability Letters, 86 (2014), 1
L. V. Rozovsky, “Small deviations of series of weighted positive random variables”, J. Math. Sci. (N. Y.), 176:2 (2011), 224–231
Rozovsky L., “Remarks on a link between the Laplace transform and distribution function of a nonnegative random variable”, Statist. Probab. Lett., 79:13 (2009), 1501–1508
Rozovsky L., “Small deviations of series of weighted i.i.d. non-negative random variables with a positive mass at the origin”, Statistics & Probability Letters, 79:13 (2009), 1495–1500
Aurzada F., “A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights”, Statist. Probab. Lett., 78:15 (2008), 2300–2307
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