Comparison theorems for small deviations of weighted series

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

Abstrakty

EN

We study comparison theorems for small deviation probabilities of weighted series and obtain more refined versions of the known comparison results. In particular, the following consequence is obtained immediately from Theorem 2.1 of the paper. Let a positive random variable X belong to the domain of attraction of a stable law with an index greater than one and let its distribution function be regularly varying at zero with an exponent β > 0. If {X_n}_n­1 are independent copies of X, and {a_n} and {b_n} are positive summable sequences such that..[formula].

Słowa kluczowe

EN

series of weighted i.i.d. positive random variables; small deviations; comparison theorems

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2012
• Tom: Vol. 32, Fasc. 1
• Strony: 117--130
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Rozovsky L. V.

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

Bibliografia

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• [8] M. A. Lifshits, Bibliography on small deviation probabilities. Available from: http://www.proba.jussieu.fr/ pageperso/smalldev/ biblio.pdf (2010). Corrections: available from http://www.webpages. uidaho. edu/ fuchang/.
• [9] V. V. Petrov, Limit theorems for sums of independent random variables (in Russian), Nauka, Moscow 1987.
• [10] L. V. Rozovsky, On small deviation probabilities for sums of independent positive random variables, J. Math. Sci. 147 (4) (2007), pp. 6935-6945.