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Stochastic Differential Equations Occurring in the Estimation of Continuous Parameter Stochastic Processes
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1969
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Nonlinear FilteringEngineeringStochastic ProcessesStochastic SystemStochastic CalculusStochastic Dynamical SystemStochastic Differential EquationStochastic AnalysisProbability TheoryStochastic SystemsStochastic IntegralsStochastic PhenomenonStochastic ControlInfinite-dimensional Stochastic ProcessesStatisticsGoogle ScholarStochastic Differential EquationsStochastic Modeling
Previous article Next article Stochastic Differential Equations Occurring in the Estimation of Continuous Parameter Stochastic ProcessesG. Kallianpur and C. StriebelG. Kallianpur and C. Striebelhttps://doi.org/10.1137/1114076PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. S. Bucy, Nonlinear filtering theory, IEEE Trans. Automatic Control, 10 (1965), CrossrefGoogle Scholar[2] J. L. Doob, Stochastic processes, J. Wiley, New York, 1962 Google Scholar[3] E. B. Dynkin, Theory of Markov processes, Translated from the Russian by D. E. Brown; edited by T. Köváry, Prentice-Hall Inc., Englewood Cliffs, N.J., 1961ix+210 MR0131900 0091.13605 Google Scholar[4] E. B. Dynkin, Markov processes. Vols. I, Translated with the authorization and assistance of the author by J. Fabius, V. Greenberg, A. Maitra, G. Majone. Die Grundlehren der Mathematischen Wi ssenschaften, Bände 121, Vol. 122, Academic Press Inc., Publishers, New York, 1965Vol. I: xii+365 MR0193671 0132.37901 CrossrefGoogle Scholar[5] D. L. Fisk, Masters Thesis, Quasi-martingales and stochastic integrals, Thesis, Michigan State University, 1963 Google Scholar[6] I. I. Gikhman and , A. V. Skorokhod, Introduction to the theory of random processes, Translated from the Russian by Scripta Technica, Inc, W. B. Saunders Co., Philadelphia, Pa., 1969xiii+516 MR0247660 Google Scholar[7] Kiyosi Ito, On stochastic differential equations, Mem. Amer. Math. Soc., 1951 (1951), 51– MR0040618 0054.05803 Google Scholar[8] K. Itô, Lectures on Stochastic Processes, Tata Institute of Fundamental Research, Bombay, 1961 Google Scholar[9] G. Kallianpur and , C. Striebel, Estimation of stochastic systems: Arbitrary system process with additive white noise observation errors, Ann. Math. Statist., 39 (1968), 785–801 MR0224242 0174.22102 CrossrefGoogle Scholar[10] R. E. Kalman and , R. S. Bucy, New results in linear filtering and prediction theory, Trans. ASME Ser. D. J. Basic Engrg., 83 (1961), 95–108 MR0234760 CrossrefGoogle Scholar[11] Harold J. Kushner, On the dynamical equations of conditional probability density functions, with applications to optimal stochastic control theory, J. Math. Anal. Appl., 8 (1964), 332–344 10.1016/0022-247X(64)90073-3 MR0161767 0126.33304 CrossrefGoogle Scholar[12] Harold J. Kushner, On the differential equations satisfied by conditional probablitity densities of Markov processes, with applications, J. Soc. Indust. Appl. Math. Ser. A Control, 2 (1964), 106–119 MR0180407 0131.16602 LinkGoogle Scholar[13] H. J. Kushner, Dynamical equations for optimal nonlinear filtering, J. Differential Equations, 3 (1967), 179–190 10.1016/0022-0396(67)90023-X MR0213182 0158.16801 CrossrefGoogle Scholar[14] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar[15] A. N. Shiryaev, On stochastic equations of the theory of conditional Markov processes, Abstract in the Theory Prob. Applications, 10 (1965), Google Scholar[16] A. V. Skorokhod, Studies in the theory of random processes, Translated from the Russian by Scripta Technica, Inc, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965viii+199 MR0185620 0146.37701 Google Scholar[17] R. L. Stratonovich, Conditional Markov processes, Theory Prob. Applications, 5 (1962), 156–178 10.1137/1105015 LinkGoogle Scholar[18] R. L. Stratonovich, A new form for stochastic integrals and equations, Vest., Moscow University, Ser. I, Matem., Mekhan., 1 (1967), 3–12 Google Scholar[19] Charlotte T. Striebel, Partial diffential equations for the conditional distribution of a Markov process given noisy observations, J. Math. Anal. Appl., 11 (1965), 151–159 10.1016/0022-247X(65)90075-2 MR0190991 0137.11804 CrossrefGoogle Scholar[20] W. M. Wonham, Some applications of stochastic differential equations to optimal nonlinear filtering, J. Soc. Indust. Appl. Math. Ser. A Control, 2 (1965), 347–369 (1965) MR0186472 0143.19004 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Backward nonlinear smoothing diffusionsТеория вероятностей и ее применения, Vol. 66, No. 2 | 22 April 2021 Cross Ref Backward Nonlinear Smoothing DiffusionsB. D. O. Anderson, A. N. Bishop, P. Del Moral, and C. 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KabanovTheory of Probability & Its Applications, Vol. 18, No. 2 | 17 July 2006AbstractPDF (316 KB)A Stochastic Differential Equation of Fisk Type for Estimation and Nonlinear Filtering ProblemsG. Kallianpur and C. StriebelSIAM Journal on Applied Mathematics, Vol. 21, No. 1 | 12 July 2006AbstractPDF (915 KB)An innovations approach to least-squares estimation--Part III: Nonlinear estimation in white Gaussian noiseIEEE Transactions on Automatic Control, Vol. 16, No. 3 | 1 Jun 1971 Cross Ref Volume 14, Issue 4| 1969Theory of Probability & Its Applications547-728 History Submitted:11 December 1967Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1114076Article page range:pp. 567-594ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics
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