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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 3, Pages 610–616
DOI: https://doi.org/10.4213/tvp5124 (Mi tvp5124) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

Small deviation probabilities of weighted sum of independent random variables with a common distribution having a power decrease in zero under minimal moment assumptions

L. V. Rozovskii

Saint-Petersburg Chemical-Pharmaceutical Academy
Full-text PDF (448 kB) Citations (3)
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DOI: https://doi.org/10.4213/tvp5124
Abstract: We represent a certain weight condition such that the exact formula for the asymptotic behavior of small deviation probabilities for weighted sum of independent random variables with a common distribution, which has a power decay at zero, is valid under optimal moment assumptions.
Keywords: small deviations, sums of independent positive random variables, slowly varying functions.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00256a
Ministry of Education and Science of the Russian Federation НШ-2504.2014.1
This research was carried out with the financial support of the Russian Science Foundation (grant 13-01-00256-a) and the Programme for Support of Leading Scientific Schools of the President of the Russian Federation (grant NSh-2504.2014.1).
Received: 09.11.2014
Revised: 21.05.2015
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 3, Pages 491–495
DOI: https://doi.org/10.1137/S0040585X97T988757
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: 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”, Teor. Veroyatnost. i Primenen., 62:3 (2017), 610–616; Theory Probab. Appl., 62:3 (2018), 491–495
Citation in format AMSBIB
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  • https://doi.org/10.4213/tvp5124
  • https://www.mathnet.ru/eng/tvp/v62/i3/p610
    • This publication is cited in the following 3 articles:
    1. Alexander Nazarov, Yulia Petrova, “L2-small ball asymptotics for Gaussian random functions: A survey”, Probab. Surveys, 20:none (2023)  crossref  mathscinet
    2. 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  mathnet  crossref  crossref  isi  elib
    3. 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  crossref  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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