Necessary and Sufficient Dynamic Programming Conditions for Continuous Time Stochastic Optimal Control
Raymond Rishel · SIAM Journal on Control · 1970
Previous article Next article Necessary and Sufficient Dynamic Programming Conditions for Continuous Time Stochastic Optimal ControlRaymond RishelRaymond Rishelhttps://doi.org/10.1137/0308040PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. G. Boltjanskii˘, Sufficient conditions for optimality and a proof of the method of dynamic programming, Izv. Akad. Nauk SSSR Ser. Mat., 28 (1964), 481–514, English transl., this Journal, 44 (1966), pp. 326–361 MR0170753 0143.32004 Google Scholar[2] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[3] 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 Google Scholar[4] E. B. Dynkin, Controlled stochastic processes—discrete parameter, Theor. Probability Appl., 10 (1966), 1–14 LinkISIGoogle Scholar[5] E. B. Dynkin, Markov processes. Vol. 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 pp. MR0193671 0132.37901 CrossrefGoogle Scholar[6] W. H. Fleming, Some Markovian optimization problems, J. Math. Mech., 12 (1963), 131–140 MR0144088 0128.37902 ISIGoogle Scholar[7] Wendell H. Fleming, Duality and a priori estimates in Markovian optimization problems, J. Math. Anal. Appl., 16 (1966), 254–279 10.1016/0022-247X(66)90170-3 MR0200082 0203.22101 CrossrefISIGoogle Scholar[8] Wendell H. Fleming, Optimal control of partially observable diffusions, SIAM J. Control, 6 (1968), 194–214 10.1137/0306015 MR0242545 0167.09104 LinkISIGoogle Scholar[9] Wendell H. Fleming, Optimal continuous-parameter stochastic control, SIAM Rev., 11 (1969), 470–509 10.1137/1011086 MR0265046 0192.52501 LinkISIGoogle Scholar[10] N. N. Krasovskii and , E. A. Lidskii, Analytic design of controls in systems with random characteristics, Parts I–III, Avtomat. i Telemekh., 22 (1961), 1145–1150, 1273–1278, 1425–1431 Google Scholar[11] Harold J. Kushner, Sufficient conditions for the optimality of a stochastic control, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 499–508 MR0192947 0138.11104 LinkGoogle Scholar[12] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar[13] S. Saks, Theory of the Integral, Hafner, New York, 1937 0017.30004 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A Universal Dynamic Program and Refined Existence Results for Decentralized Stochastic ControlSerdar YükselSIAM Journal on Control and Optimization, Vol. 58, No. 5 | 8 September 2020AbstractPDF (519 KB)Continuous-Time Stochastic Averaging on the Infinite Interval for Locally Lipschitz SystemsSIAM Journal on Control and Optimization, Vol. 48, No. 5 | 3 March 2010AbstractPDF (543 KB)Approximation and Limit Results for Nonlinear Filters Over an Infinite Time IntervalSIAM Journal on Control and Optimization, Vol. 37, No. 6 | 26 July 2006AbstractPDF (499 KB)Semimartingale Models of Stochastic Optimal Control, with Applications to Double MartingalesSIAM Journal on Control and Optimization, Vol. 18, No. 5 | 18 July 2006AbstractPDF (2252 KB)An Introductory Approach to Duality in Optimal Stochastic ControlSIAM Review, Vol. 20, No. 1 | 10 July 2006AbstractPDF (1413 KB)Optimal Control of Jump ProcessesSIAM Journal on Control and Optimization, Vol. 15, No. 1 | 18 July 2006AbstractPDF (2539 KB)On the Existence of Optimal Policies in Stochastic ControlSIAM Journal on Control, Vol. 11, No. 4 | 18 July 2006AbstractPDF (633 KB)Dynamic Programming Conditions for Partially Observable Stochastic SystemsSIAM Journal on Control, Vol. 11, No. 2 | 18 July 2006AbstractPDF (2347 KB)Necessary and Sufficient Conditions for Optimal Control of Semi-Markov Jump ProcessesSIAM Journal on Control, Vol. 11, No. 2 | 18 July 2006AbstractPDF (1135 KB) Volume 8, Issue 4| 1970SIAM Journal on Control441-605 History Submitted:14 July 1969Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0308040Article page range:pp. 559-571ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics