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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm3876https://doi.org/10.1070/SM1977v033n02ABEH002421 https://www.mathnet.ru/eng/sm/v146/i2/p227
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Abstract page: | 556 | Russian version PDF: | 147 | English version PDF: | 26 | References: | 75 | First page: | 2 |
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