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Mathematics of the USSR-Sbornik, 1977, Volume 33, Issue 2, Pages 203–221
DOI: https://doi.org/10.1070/SM1977v033n02ABEH002421 (Mi sm3876) 		 
This article is cited in 36 scientific papers (total in 36 papers)

On the question of absolute continuity and singularity of probability measures

Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev
English version PDF (948 kB) Citations (36)
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DOI: https://doi.org/10.1070/SM1977v033n02ABEH002421
Abstract: The basic result in this paper (Theorem 1) generalizes the well-known criterion of Kakutani to measures corresponding to arbitrary random sequences. The proof is based on Theorem 6, which gives a description of the set of convergence of a submartingale with bounded increments. The question of absolute continuity and singularity of measures corresponding to solutions of stochastic difference equations is studied. The dichotomy for Gaussian measures is obtained as a corollary.
Bibliography: 13 titles.
Received: 17.03.1977
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1977, Volume 104(146), Number 2(10), Pages 227–247
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: Primary 60G30; Secondary 28A35, 60F20, 60G15, 60G45, 60G50, 60J10
Language: English
Original paper language: Russian
Citation: Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev, “On the question of absolute continuity and singularity of probability measures”, Mat. Sb. (N.S.), 104(146):2(10) (1977), 227–247; Math. USSR-Sb., 33:2 (1977), 203–221
Citation in format AMSBIB
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\by Yu.~M.~Kabanov, R.~Sh.~Liptser, A.~N.~Shiryaev
\paper On the question of absolute continuity and singularity of probability measures
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 104(146)
\issue 2(10)
\pages 227--247
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=517732}
\zmath{https://zbmath.org/?q=an:0375.60048|0398.60044}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 33
\issue 2
\pages 203--221
\crossref{https://doi.org/10.1070/SM1977v033n02ABEH002421}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1977GR63000003}
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  • https://www.mathnet.ru/eng/sm/v146/i2/p227
    • This publication is cited in the following 36 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:557
    Russian version PDF:147
    English version PDF:26
    References:75
    First page:2
     
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