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100   $a20140602d2014      u|             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aGeneral Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions$b[electronic resource] /$fby Qi Lü, Xu Zhang
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (148 p.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8201
300   $aDescription based upon print version of record.
311   $a1-322-13565-7 
311   $a3-319-06631-5 
320   $aIncludes bibliographical references.
327   $aPreface; 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;  References
330   $aThe classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagintype maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.
410  0$aSpringerBriefs in Mathematics,$x2191-8201
606   $aSystem theory
606   $aControl theory
606   $aMathematical optimization
606   $aCalculus of variations
606   $aProbabilities
606   $aSocial sciences?Mathematics
606   $aStatistics
606   $aSystems Theory, Control 
606   $aCalculus of Variations and Optimization
606   $aProbability Theory
606   $aMathematics in Business, Economics and Finance
606   $aStatistics
615  0$aSystem theory.
615  0$aControl theory.
615  0$aMathematical optimization.
615  0$aCalculus of variations.
615  0$aProbabilities.
615  0$aSocial sciences?Mathematics.
615  0$aStatistics.
615 14$aSystems Theory, Control .
615 24$aCalculus of Variations and Optimization.
615 24$aProbability Theory.
615 24$aMathematics in Business, Economics and Finance.
615 24$aStatistics.
676   $a519.3
700   $aLü$b Qi$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721607
702   $aZhang$b Xu$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299966403321
996   $aGeneral Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions$92544379
997   $aUNINA