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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 1, Pages 78–103 (Mi tvp302)  

This article is cited in 5 scientific papers (total in 5 papers)

Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cramér condition

L. V. Rozovskii

Saint-Petersburg Chemical-Pharmaceutical Academy

Abstract: This paper studies the asymptotic behavior of a density of a sum of independent identically distributed random variables with a common absolutely continuous distribution satisfying the right-hand Cramér condition. We prove that for a definite class of such distributions the well-known asymptotic representations in local and integral limit theorems are valid in the case of large deviations of arbitrarily high order.

Keywords: independent random variables, density function, large deviations, Cramér condition.

DOI: https://doi.org/10.4213/tvp302

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English version:
Theory of Probability and its Applications, 2004, 48:1, 108–130

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Received: 20.12.2000

Citation: L. V. Rozovskii, “Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cramér condition”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 78–103; Theory Probab. Appl., 48:1 (2004), 108–130

Citation in format AMSBIB
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\pages 78--103
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\jour Theory Probab. Appl.
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\issue 1
\pages 108--130
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Borovkov, A. A. Mogul'skii, “On large and superlarge deviations for sums of independent random vectors under the Cramer condition. I”, Theory Probab. Appl., 51:2 (2007), 227–255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. L. V. Rozovskii, “Superlarge deviation probabilities for sums of independent random variables with exponential decreasing distribution”, Theory Probab. Appl., 52:1 (2008), 167–171  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. L. V. Rozovsky, “Small deviation probabilities for sums of independent positive random variables, whose density has a power decay at zero”, J. Math. Sci. (N. Y.), 188:6 (2013), 748–752  mathnet  crossref  mathscinet
    4. L. V. Rozovskii, “Superlarge deviation probabilities for sums of independent random variables with exponential decreasing distributions. II”, Theory Probab. Appl., 59:1 (2015), 168–177  mathnet  crossref  crossref  mathscinet  isi  elib
    5. L. V. Rozovskii, “Ob asimptotike svertki raspredelenii s regulyarno eksponentsialno ubyvayuschimi khvostami”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 265–274  mathnet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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