On the Existence of Optimal Stochastic Controls

Previous article Next article On the Existence of Optimal Stochastic ControlsHarold J. KushnerHarold J. Kushnerhttps://doi.org/10.1137/0303031PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Harold J. Kushner, On the stochastic maximum principle with “average” constraints, J. Math. Anal. Appl., 12 (1965), 13–26 10.1016/0022-247X(65)90050-8 MR0195631 0161.07203 CrossrefISIGoogle Scholar[2] L. S. Pontryagin, , V. G. Boltyanskii, , R. V. Gamkrelidze and , E. F. Mishchenko, The mathematical theory of optimal processes, Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt, Interscience Publishers John Wiley & Sons, Inc. New York-London, 1962viii+360 MR0166037 0102.32001 Google Scholar[3] E. B. Lee and , L. Markus, Optimal control for nonlinear processes, Arch. Rational Mech. Anal., 8 (1961), 36–58 MR0128571 0099.08703 CrossrefISIGoogle Scholar[4] Emilio Roxin, The existence of optimal controls, Michigan Math. J., 9 (1962), 109–119 10.1307/mmj/1028998668 MR0136844 0105.07801 CrossrefGoogle Scholar[5] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[6] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar[7] Richard Datko, An implicit function theorem with an application to control theory, Michigan Math. J., 11 (1964), 345–351 10.1307/mmj/1028999188 MR0170747 0127.28002 CrossrefGoogle Scholar[8] Nelson Dunford and , Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York, 1958xiv+858 MR0117523 0084.10402 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the Solutions of a Stochastic Control SystemTyrone Duncan and Pravin Varaiya18 July 2006 | SIAM Journal on Control, Vol. 9, No. 3AbstractPDF (1274 KB)Existence of Optimal Stochastic Control LawsV. E. Beneš18 July 2006 | SIAM Journal on Control, Vol. 9, No. 3AbstractPDF (2150 KB)Existence of Optimal Strategies Based on Specified Information, for a Class of Stochastic Decision ProblemsV. E. Beneš18 July 2006 | SIAM Journal on Control, Vol. 8, No. 2AbstractPDF (899 KB)Optimal Continuous-Parameter Stochastic ControlWendell H. Fleming18 July 2006 | SIAM Review, Vol. 11, No. 4AbstractPDF (4487 KB) Volume 3, Issue 3| 1965Journal of the Society for Industrial and Applied Mathematics Series A Control History Submitted:20 June 1964Accepted:09 August 1965Published online:18 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0303031Article page range:pp. 463-474ISSN (print):0887-4603ISSN (online):2168-359XPublisher:Society for Industrial and Applied Mathematics