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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 368, Pages 201–228 (Mi znsl3514)  
This article is cited in 6 scientific papers (total in 6 papers)

The theorems about stochastic integral distributions convergence to signed measures and the local limit theorems for large deviations

N. V. Smorodina, M. M. Faddeev

Saint-Petersburg State University, Saint-Petersburg, Russia
Full-text PDF (678 kB) Citations (6)
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Abstract: We study properties of symmetric stable measures with index $\alpha>2$, $\alpha\neq2m$, $m\in\mathbb N$. 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. Bibl. – 11 titles.
Key words and phrases: Poisson random measures, Lévy–Khinchin representation, strictly stable random variable, limit theorems.
Received: 10.10.2009
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 167, Issue 4, Pages 550–565
DOI: https://doi.org/10.1007/s10958-010-9943-8
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: N. V. Smorodina, M. M. Faddeev, “The theorems about stochastic integral distributions convergence to signed measures and the local limit theorems for large deviations”, Probability and statistics. Part 15, Zap. Nauchn. Sem. POMI, 368, POMI, St. Petersburg, 2009, 201–228; J. Math. Sci. (N. Y.), 167:4 (2010), 550–565
Citation in format AMSBIB
\Bibitem{SmoFad09}
\by N.~V.~Smorodina, M.~M.~Faddeev
\paper The theorems about stochastic integral distributions convergence to signed measures and the local limit theorems for large deviations
\inbook Probability and statistics. Part~15
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 368
\pages 201--228
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3514}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 167
\issue 4
\pages 550--565
\crossref{https://doi.org/10.1007/s10958-010-9943-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953915208}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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