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Theory of Stochastic Processes, 2010, Volume 16(32), Issue 1, Pages 94–102 (Mi thsp65)  
Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem

N. V. Smorodina, M. M. Faddeev

St. Petersburg State University, St.-Petersburg, Russia
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Abstract: We study properties of symmetric stable measures with index $\alpha>2,\ \ \alpha\neq 2k,\ k\in\mathbb{N}$. 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.
Keywords: Large deviation problem, strictly stable random variable, limit theorems.
Funding agency Grant number
Deutsche Forschungsgemeinschaft 436 RUS 113/823
Russian Foundation for Basic Research 09-01-00515a
Ministry of Education and Science of the Russian Federation 638.2008.1
816.2008.1
This paper was partly supported by DFG 436 RUS 113/823, NSh 638.2008.1. The second author was supported by the Russian Foundation for Basic Research 09-01-00515a, Nsh 816.2008.1.
Bibliographic databases:
Document Type: Article
MSC: 28C20, 60H05, 60G57
Language: English
Citation: N. V. Smorodina, M. M. Faddeev, “Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem”, Theory Stoch. Process., 16(32):1 (2010), 94–102
Citation in format AMSBIB
\Bibitem{SmoFad10}
\by N.~V.~Smorodina, M.~M.~Faddeev
\paper Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem
\jour Theory Stoch. Process.
\yr 2010
\vol 16(32)
\issue 1
\pages 94--102
\mathnet{http://mi.mathnet.ru/thsp65}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2779835}
\zmath{https://zbmath.org/?q=an:1224.28032}
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