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Theorems on convergence of stochastic integrals distributions to signed measures and local limit theorems for large deviations

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We study properties of symmetric stable measures with index α > 2, α ≠ 2m, \( m \in \mathbb{N} \). Such measures are signed ones, and hence they are not probability measures. For this class of measures, we construct an analogue of the Lévy–Khinchin representation. We show that, in some sense, these signed measures are limit measures for sums of independent random variables. Bibliography: 11 titles.

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References

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Authors and Affiliations

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

    N. V. Smorodina & M. M. Faddeev

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  1. N. V. Smorodina
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  2. M. M. Faddeev
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Correspondence to N. V. Smorodina.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 368, 2009, pp. 201–228.

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Smorodina, N.V., Faddeev, M.M. Theorems on convergence of stochastic integrals distributions to signed measures and local limit theorems for large deviations. J Math Sci 167, 550–565 (2010). https://doi.org/10.1007/s10958-010-9943-8

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  • DOI: https://doi.org/10.1007/s10958-010-9943-8

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