Small deviation probabilities of weighted sums with fast decreasing weights

• Autorzy: Rozovsky L. V.
• Języki publikacji: EN

Abstrakty

EN

We examine small deviation probabilities of weighted sums of i.i.d. positive random variables whose distribution function is regularly varying at zero provided that weights are decreasing fast enough.

Słowa kluczowe

EN

small deviation probabilities; i.i.d. positive random variables; weighted sums; slowly varying functions; regularly varying functions

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 1
• Strony: 161--178
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Rozovsky L. V.

• St. Petersburg Chemical-Pharmaceutical Academy, Department of Mathematics, Prof. Popova Street, 14, 197376, St. Petersburg, Russia

Bibliografia

• [1] N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge 1987.
• [2] A. A. Borovkov and P. S. Ruzankin, On small deviations of series of weighted random variables, J. Theoret. Probab. 21 (3) (2008), pp. 628-649.
• [3] A. A. Borovkov and P. S. Ruzankin, Small deviations of series of independent positive random variables with weights close to exponential, Siberian Adv. Math. 18 (3) (2008), pp. 163-175.
• [4] T. Dunker, M. A. Lifshits, and W. Linde, Small deviation probabilities of sums of independent random variables, in: High Dimensional Probability, Progr. Probab., Vol. 43, Birkhäuser, Basel 1998, pp. 59-74.
• [5] M. A. Lifshits, On the lower tail probabilities of some random series, Ann. Probab. 25 (1) (1997), pp. 424-442.
• [6] M. A. Lifshits, Bibliography on small deviation probabilities, Available on http://www.proba.jussieu.fr/pageperso/smalldev/biblio.pdf (2010).
• [7] A. I. Nazarov, Log-level comparison principle for small ball probabilities, Statist. Probab. Lett. 79 (4) (2009), pp. 481-486.
• [8] V. V. Petrov, Limit theorems for sums of independent random variables (in Russian), Nauka, Moscow 1987.
• [9] L. V. Rozovsky, On small deviation probabilities for sums of independent positive random variables, J. Math. Sci. 147 (4) (2007), pp. 6935-6945.
• [10] L. V. Rozovsky, Remarks on a link between Laplace transform and distribution function of a nonnegative random variable, Statist. Probab. Lett. 79 (2009), pp. 1501-1508.
• [11] L. V. Rozovsky, Small deviations of series of weighted i.i.d. non-negative random variables with a positive mass at the origin, Statist. Probab. Lett. 79 (2009), pp. 1495-1500.
• [12] L. V. Rozovsky, Comparison theorems for small deviations of weighted series, Probab. Math. Statist. 32 (1) (2012), pp. 117-130.
• [13] L. V. Rozovsky, Small deviations of series of independent non-negative random variables with smooth weights (in Russian), Teor. Veroyatnost. Primenen. 58 (1) (2013), pp. 133-151.
• [14] L. V. Rozovsky, Small deviation probabilities of weighted sums under minimal moment assumptions, Statist. Probab. Lett. 86 (1) (2014), pp. 1-6.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).