04285nam 22008295 450 991029996640332120230412152509.03-319-06632-310.1007/978-3-319-06632-5(CKB)3710000000121884(EBL)1782955(SSID)ssj0001275822(PQKBManifestationID)11718521(PQKBTitleCode)TC0001275822(PQKBWorkID)11236467(PQKB)10177985(MiAaPQ)EBC1782955(DE-He213)978-3-319-06632-5(PPN)179764497(EXLCZ)99371000000012188420140602d2014 u| 0engur|n|---|||||txtccrGeneral Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions /by Qi Lü, Xu Zhang1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (148 p.)SpringerBriefs in Mathematics,2191-8201Description based upon print version of record.1-322-13565-7 3-319-06631-5 Includes bibliographical references.Preface; Acknowledgments; Contents; 1 Introduction; 2 Preliminaries; 3 Well-Posedness of the Vector-Valued BSEEs; 4 Well-Posedness Result for the Operator-Valued BSEEs with Special Data; 5 Sequential Banach-Alaoglu-Type Theorems in the Operator Version; 6 Well-Posedness of the Operator-Valued BSEEs in the General Case; 7 Some Properties of the Relaxed Transposition Solutions to the Operator-Valued BSEEs; 8 Necessary Condition for Optimal Controls, the Case of Convex Control Domains; 9 Necessary Condition for Optimal Controls, the Case of Non-convex Control Domains; ReferencesThe classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagintype maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.SpringerBriefs in Mathematics,2191-8201System theoryControl theoryMathematical optimizationCalculus of variationsProbabilitiesSocial sciences—MathematicsStatisticsSystems Theory, Control Calculus of Variations and OptimizationProbability TheoryMathematics in Business, Economics and FinanceStatisticsSystem theory.Control theory.Mathematical optimization.Calculus of variations.Probabilities.Social sciences—Mathematics.Statistics.Systems Theory, Control .Calculus of Variations and Optimization.Probability Theory.Mathematics in Business, Economics and Finance.Statistics.519.3Lü Qiauthttp://id.loc.gov/vocabulary/relators/aut721607Zhang Xuauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299966403321General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions2544379UNINA