On the Behavior of the Likelihood Ratio of Semimartingales

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Previous article Next article On the Behavior of the Likelihood Ratio of SemimartingalesA. F. TaraskinA. F. Taraskinhttps://doi.org/10.1137/1129060PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. I. Gikhman and , A. V. Skorokhod, Theory of Stochastic Processes, Vol. 3, Vol. 210, Springer, New York, 1979 CrossrefGoogle Scholar[2] Yu. M. Kabanov, , R. Sh. Liptser and , A. N. Shiryaev, Absolute continuity and singularity of locally absolutely continuous probability distributions. I, Mat. Sb. (N.S.), 107(149) (1978), 364–415, 463, (In Russian.) 80e:60056a Yu. M. Kabanov, , R. Sh. Liptser and , A. N. Shiryaev, Absolute continuity and singularity of locally absolutely continuous probability distributions. II, Mat. Sb. (N.S.), 108(150) (1979), 32–61, 143, (In Russian.) 80e:60056b Google Scholar[3] G. Roussas, Contiguity of probability measures: some applications in statistics, Cambridge University Press, London, 1972xiii+248 50:11554 0265.60003 CrossrefGoogle Scholar[4] R. Sh. Liptser and , A. N. Shiryaev, Weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments, Mat. Sb. (N.S.), 116(158) (1981), 331–358, 463, (In Russian.) 84b:60041 0484.60024 Google Scholar[5] R. SH. Liptser and , A. An. Shiryaev, Statistics of Random Processes, Springer, New York, 1977–1978 CrossrefGoogle Scholar[6] I. A. Ibragimov and , R. Z. Khas'minskii, Statistical estimation, Applications of Mathematics, Vol. 16, Springer-Verlag, New York, 1981vii+403, Asymptotic Theory 82g:62006 0467.62026 CrossrefGoogle Scholar[7] A. F. Taraskin, On convergence of distributions of certain local martingales, Third Vil'nyus International Conference on Probability Theory and Mathematical Statistics, Vol. 2, Institute of Mathematics and Cybernetics of the Lithuanian SSR Academy of Sciences, Vil'nyus, 1981, 182–183, (In Russian.) Google Scholar[9] A. F. Taraskin, Connection of Shannon and Fisher information in a diffusion process, Problemy Peredachi Informatsii, 15 (1979), 14–26, (In Russian.) Google Scholar[10] Yu. N. Lin'kov, Asymptotic properties of statistical estimates and criteria for Markov processes, Theory of Probability and Mathematical Statistics, Vol. 25, Kiev Univ. Press, Kiev, 76–91, (In Russian.) Google Scholar[11] Yu. A. Kutoyants, On a problem of testing hypotheses and asymptotic normality of statistic integrals, Theory Prob. Appl., 20 (1975), 376–384 0331.62063 LinkGoogle Scholar[12] Lucien Le Cam, Locally asymptotically normal families of distributions. Certain approximations to families of distributions and their use in the theory of estimation and testing hypotheses, Univ. california Publ. Statist., 3 (1960), 37–98 23:A4197 Google Scholar[13] B. Grigelionis, Masters Thesis, Investigations in the theory of random processes (optimal stopping, effective Markov criteria), Competitive doctoral dissertation in physical and mathematical sciences, Institute of Physics and Mathematics of the Lithuanian SSR Academy of Sciences, Vil'nyus, 1969, 276 pages., (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Stable convergence of the log-likelihood ratio to a mixture of infinitely divisible distributionsJournal of Mathematical Sciences, Vol. 84, No. 3 | 1 Apr 1997 Cross Ref Asymptotic mixed normality and hellinger processesStochastics and Stochastic Reports, Vol. 48, No. 3-4 | 4 April 2007 Cross Ref Local asymptotic mixed normality for semimartingale experimentsProbability Theory and Related Fields, Vol. 92, No. 2 | 1 Jun 1992 Cross Ref Volume 29, Issue 3| 1985Theory of Probability & Its Applications History Submitted:23 October 1982Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1129060Article page range:pp. 452-464ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics