Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 145-166
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N. V. Smorodina; M. M. Faddeev. Lévy–Khinchin representation of a class of signed measures. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 145-166. http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a10/
@article{ZNSL_2008_361_a10,
author = {N. V. Smorodina and M. M. Faddeev},
title = {L\'evy{\textendash}Khinchin representation of a~class of signed measures},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {145--166},
year = {2008},
volume = {361},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a10/}
}
TY - JOUR
AU - N. V. Smorodina
AU - M. M. Faddeev
TI - Lévy–Khinchin representation of a class of signed measures
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2008
SP - 145
EP - 166
VL - 361
UR - http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a10/
LA - ru
ID - ZNSL_2008_361_a10
ER -
%0 Journal Article
%A N. V. Smorodina
%A M. M. Faddeev
%T Lévy–Khinchin representation of a class of signed measures
%J Zapiski Nauchnykh Seminarov POMI
%D 2008
%P 145-166
%V 361
%U http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a10/
%G ru
%F ZNSL_2008_361_a10
We study properties of symmetric stable measures with the index of stability $\alpha\in(2,4)\cup(4,6)$. For such signed measures we construct a natural analogue of the Lévy–Khinchin representation. We show that in some special sense these measures are limit measures for the sums of independent random variables. Bibl. – 6 titles.
[1] A. V. Skorokhod, Sluchainye protsessy s nezavisimymi prirascheniyami, Nauka, Moskva, 1986 | MR | Zbl
[2] 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 | MR | Zbl
[3] 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
[4] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Nauka, Moskva, 1958
[5] I. A. Ibragimov, Yu. V. Linnik, Nezavisimye i statsionarno svyazannye sluchainye velichiny, Nauka, Moskva, 1965
[6] M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovykh prostranstvakh, Izd-vo LGU, Leningrad, 1980 | MR