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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 339, Pages 135–150 (Mi znsl162)  

This article is cited in 4 scientific papers (total in 4 papers)

The invariant and quasi-invariant transformations of the stable processes with independent increments

N. V. Smorodina

Saint-Petersburg State University
Full-text PDF (225 kB) Citations (4)
References:
Abstract: Let $\xi(t)$, $t\in[0,1]$ be a strictly stable process with the index of stability $\alpha\in(0,2)$. By $\mathcal P_\xi$ we denote the law of $\xi$ in the Skorokhod space $\mathbb D[0,1]$. For arbitrary strictly stable process $\xi$ we construct $\mathcal P_\xi-$quasi-invariant semigroup of transformations of $\mathbb D[0,1]$. For strictly stable processes with positive and negative jumps we construct $\mathcal P_\xi-$quasi-invariant group of transformations of $\mathbb D[0,1]$. In symmetric case this group is a group of the invariant transformations.
Received: 11.11.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 145, Issue 2, Pages 4914–4922
DOI: https://doi.org/10.1007/s10958-007-0325-9
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: N. V. Smorodina, “The invariant and quasi-invariant transformations of the stable processes with independent increments”, Probability and statistics. Part 10, Zap. Nauchn. Sem. POMI, 339, POMI, St. Petersburg, 2006, 135–150; J. Math. Sci. (N. Y.), 145:2 (2007), 4914–4922
Citation in format AMSBIB
\Bibitem{Smo06}
\by N.~V.~Smorodina
\paper The invariant and
quasi-invariant transformations of the stable processes
with independent increments
\inbook Probability and statistics. Part~10
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 339
\pages 135--150
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl162}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2355406}
\zmath{https://zbmath.org/?q=an:1129.60044}
\elib{https://elibrary.ru/item.asp?id=9305309}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 145
\issue 2
\pages 4914--4922
\crossref{https://doi.org/10.1007/s10958-007-0325-9}
\elib{https://elibrary.ru/item.asp?id=13547320}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547655645}
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  • https://www.mathnet.ru/eng/znsl/v339/p135
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
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    Full-text PDF :55
    References:48
     
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