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Mat. Sb. (N.S.), 1979, Volume 108(150), Number 1, Pages 32–61 (Mi msb2258)  

This article is cited in 21 scientific papers (total in 21 papers)

Absolute continuity and singularity of locally absolutely continuous probability distributions. II

Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev


Abstract: The second part of this study deals with criteria for the absolute continuity of measures for various classes of random processes, starting out from the general results in Part I. We consider processes with independent increments, semimartingales, multivariate point processes, Gaussian processes, Markov chains, and processes with a countable number of states.
Bibliography: 33 titles.

Full text: PDF file (2426 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1980, 36:1, 31–58

Bibliographic databases:

UDC: 519.2
MSC: Primary 60G30, 60G44; Secondary 28C20, 60G15, 60G25, 60G40, 60H05, 60J27, 60J30
Received: 11.01.1978

Citation: Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev, “Absolute continuity and singularity of locally absolutely continuous probability distributions. II”, Mat. Sb. (N.S.), 108(150):1 (1979), 32–61; Math. USSR-Sb., 36:1 (1980), 31–58

Citation in format AMSBIB
\Bibitem{KabLipShi79}
\by Yu.~M.~Kabanov, R.~Sh.~Liptser, A.~N.~Shiryaev
\paper Absolute continuity and singularity of locally absolutely continuous probability distributions.~II
\jour Mat. Sb. (N.S.)
\yr 1979
\vol 108(150)
\issue 1
\pages 32--61
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=524211}
\zmath{https://zbmath.org/?q=an:0448.60028|0427.60037}
\transl
\jour Math. USSR-Sb.
\yr 1980
\vol 36
\issue 1
\pages 31--58
\crossref{https://doi.org/10.1070/SM1980v036n01ABEH001760}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. I. Gal'chuk, “Optional martingales”, Math. USSR-Sb., 40:4 (1981), 435–468  mathnet  crossref  mathscinet  zmath  isi
    2. Melnikov A., Hadziev D., “Asymptotics of Small Deviations Probability for Gaussian Martingales”, 34, no. 11, 1981, 1485–1486  mathscinet  isi
    3. Hadziev D., “Gaussian Solutions of Some Stochastic-Equations”, 34, no. 12, 1981, 1647–1649  mathscinet  zmath  isi
    4. Shiryayev A., “Martingales - Recent Developments, Results and Applications”, Int. Stat. Rev., 49:3 (1981), 199–233  crossref  mathscinet  isi
    5. A. A. Butov, “The equivalence of measures corresponding to canonical Gaussian processes”, Russian Math. Surveys, 37:5 (1982), 162–163  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Yu. M. Kabanov, “On the existence of a solution in a problem of controlling a counting process”, Math. USSR-Sb., 47:2 (1984), 425–438  mathnet  crossref  mathscinet  zmath
    7. Chitashvili R., “Martingale Ideology in the Theory of Controlled Stochastic-Processes”, 1021, 1983, 73–92  mathscinet  zmath  isi
    8. Glonti O., “Transmission of Television Type Signals Through a Feedback Channel”, 1021, 1983, 157–166  mathscinet  zmath  isi
    9. Kabanov I. Liptser R. Shiriaev A., “Estimates of Proximity in the Variation of Probability-Measures”, 278, no. 2, 1984, 265–268  mathscinet  zmath  isi
    10. A. F. Taraskin, “On the limiting behaviour of the likelihood ratio for semimartingales”, Russian Math. Surveys, 40:2 (1985), 237–238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. Memin J. Shiryayev A., “Hellinger-Kakutani Distance in Laws Corresponding to 2 Processes with Independent Increments”, 70, no. 1, 1985, 67–89  crossref  mathscinet  zmath  isi
    12. Musiela M., “Divergence, Convergence and Moments of Some Integral Functionals of Diffusions”, 70, no. 1, 1985, 49–65  crossref  mathscinet  zmath  isi
    13. Musiela M., “On Kac Functionals of One-Dimensional Diffusions”, Stoch. Process. Their Appl., 22:1 (1986), 79–88  crossref  mathscinet  zmath  isi
    14. Kabanov Y. Liptser R. Shiryaev A., “On the Variation Distance for Probability-Measures Defined on a Filtered Space”, Probab. Theory Relat. Field, 71:1 (1986), 19–35  crossref  mathscinet  zmath  isi
    15. Knut K. Aase, Peter Guttorp, “Estimation in models for security prices”, Scandinavian Actuarial Journal, 1987:3-4 (1987), 211  crossref
    16. V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Russian Math. Surveys, 45:3 (1990), 1–104  mathnet  crossref  mathscinet  zmath  isi
    17. A.R. Darwich, “About the absolute continuity and orthogonality for two probability measures”, Statistics & Probability Letters, 52:1 (2001), 1  crossref
    18. Galtchouk L., “Optimality of the Wald Sprt for Processes with Continuous Time Parameter”, Moda6 Advances in Model-Oriented Design and Analysis, Contributions to Statistics, eds. Atkinson A., Hackl P., Muller W., Physica-Verlag Gmbh & Co, 2001, 97–110  crossref  mathscinet  isi
    19. A. A. Gushchin, É. Mordecki, “Bounds on Option Prices for Semimartingale Market Models”, Proc. Steklov Inst. Math., 237 (2002), 73–113  mathnet  mathscinet  zmath
    20. S. S. Gabriyelyan, “Absolute Continuity and Singularity of Two Probability Measures on a Filtered Space”, J Theor Probab, 2011  crossref
    21. F. Klebaner, R. Liptser, “When a stochastic exponential is a true martingale. Extension of the Beneš method”, Theory Probab. Appl., 58:1 (2014), 38–62  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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