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Local limit theorems for large deviations

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We study properties of stable measures with index α > 2, α ∉ ℕ. Such measures are signed ones, and hence, they are not probability measures. We show that in some sense, these signed measures are limit measures for sums of independent random variables. In the last section of the paper, we prove a theorem about large deviations of sums of independent random variables using the positive part of the limit measure. Bibliography: 8 titles.

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References

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    D. V. Batkovich

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  1. D. V. Batkovich
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Correspondence to D. V. Batkovich.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 396, 2011, pp. 7–30.

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Batkovich, D.V. Local limit theorems for large deviations. J Math Sci 188, 641–654 (2013). https://doi.org/10.1007/s10958-013-1154-7

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  • DOI: https://doi.org/10.1007/s10958-013-1154-7

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