Geodesic
The theorems about stochastic integral distributions convergence to signed measures and the local limit theorems for large deviations
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 201-228 
N. V. Smorodina; M. M. Faddeev. The theorems about stochastic integral distributions convergence to signed measures and the local limit theorems for large deviations. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 201-228. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a15/
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     title = {The theorems about stochastic integral distributions convergence to signed measures and the local limit theorems for large deviations},
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     year = {2009},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a15/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] S. Albeverio, N. Smorodina, “A Distributional approach to multiple stochastic integrals and transformations of the Poisson measure”, Acta Appl. Math., 94 (2006), 1–19 | DOI | MR | Zbl

[2] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Nauka, M., 1958 | Zbl

[3] V. M. Zolotarev, Odnomernye ustoichivye raspredeleniya, Nauka, M., 1983 | MR | Zbl

[4] I. A. Ibragimov, Yu. V. Linnik, Nezavisimye i statsionarno svyazannye sluchainye velichiny, Nauka, M., 1965

[5] S. V. Nagaev, “Large deviations of sums of independent random variables”, Ann. Prob., 7:5 (1979), 745–789 | DOI | MR | Zbl

[6] S. V. Nagaev, “Lokalnye predelnye teoremy dlya bolshikh uklonenii”, Teor. veroyatn. i ee primen., 5:2 (1960), 259–261

[7] S. V. Nagaev, “Lokalnye predelnye teoremy dlya bolshikh uklonenii”, Vestnik LGU. Seriya matem., mekhan., astron., 1962, no. 1, 80–88 | MR | Zbl

[8] A. V. Skorokhod, Sluchainye protsessy s nezavisimymi prirascheniyami, Nauka, M., 1986 | MR | Zbl

[9] N. V. Smorodina, “Asimptoticheskoe razlozhenie dlya raspredeleniya gladkogo odnorodnogo funktsionala ot strogo ustoichivogo sluchainogo vektora. II”, Teoriya veroyatn. i ee primen., 44:2 (1999), 458–465 | DOI | MR | Zbl

[10] N. Smorodina, M. Faddeev, “The Lévy–Khinchin representation of the one class of signed stable measures and some its applications”, Acta Appl. Math. | DOI | MR

[11] L. Shvarts, Matematicheskie metody dlya fizicheskikh nauk, Mir, M., 1965 | MR