Filtering, Smoothing and Prediction of Degenerate Diffusion Processes. Backward Equations
Boris L. Rozovskii · Theory of Probability and Its Applications · 1984
Previous article Next article Filtering, Smoothing and Prediction of Degenerate Diffusion Processes. Backward EquationsB. L. RozovskiiB. L. Rozovskiihttps://doi.org/10.1137/1128074PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. Sh. Liptser and , A. N. Shiryaev, Statistics of random processes. I, Springer-Verlag, New York, 1977x+394 57:14125 R. Sh. Liptser and , A. N. Shiryaev, Statistics of random processes. II, Springer-Verlag, New York, 1978x+339 58:7827 CrossrefGoogle Scholar[2] G. Kallianpur, Stochastic filtering theory, Applications of Mathematics, Vol. 13, Springer-Verlag, New York, 1980xvi+316 82f:60089 0458.60001 CrossrefGoogle Scholar[3] N. V. Krylov and , B. L. Rozovskii, On conditional distributions of diffusion processes, Math. USSR-Izvestia, 12 (1978), 336–356 0402.60077 CrossrefGoogle Scholar[4] B. L. Rozovskii, On conditional distributions of degenerate diffusion processes, Theory Prob. Appl., 25 (1980), 147–154 LinkGoogle Scholar[5] H. J. Kushner, Probability methods for approximations in stochastic control and for elliptic equations, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1977xvii+243 57:9258 0547.93076 Google Scholar[6] E. Pardoux, Stochastic partial differential equations and filtering of diffusion processes, Stochastics, 3 (1979), 127–167 81b:60059 0424.60067 CrossrefGoogle Scholar[7] E. Pardoux, Equations du filtrate non-linéaire de la prédiction et du lissage, 1980, prepublication de l'Université de Provence, Marseilles Google Scholar[8] N. V. Krylov, Controlled diffusion processes, Applications of Mathematics, Vol. 14, Springer-Verlag, New York, 1980xii+308 82a:60062 CrossrefGoogle Scholar[9] Yu. N. Blagoveshchenskii and , M. I. Freidlin, Certain properties of diffusion processes depending on a parameter, Soviet Math. Doklady, 2 (1961), 633–639 Google Scholar[10] M. Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685, 3rd ed. 34:3596 0108.14202 Google Scholar[11] N. V. Krylov and , B. L. Rozovskii, On the properties of degenerate parabolic Itô equations of second order, Trudy I. G. Petrovskii Seminar, Vol. 8, Izd-vo, MSU, Moscow, 1982, 153–168, (In Russian.) Google Scholar[12] N. V. Krylov, Some new results on the theory of controlled diffusion processes, Math. USSR—Sbornik, 37 (1980), 133–149 0436.93055 CrossrefGoogle Scholar[13] V. I. Arnol'd, Mathematical Methods of Classical Mechanics, Nauka, Moscow, 1979, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Volume 28, Issue 4| 1984Theory of Probability & Its Applications657-861 History Submitted:01 July 1981Published online:28 July 2006 InformationCopyright © 1984 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1128074Article page range:pp. 762-774ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics