随机控制

图书标准信息

• 作者 雍炯敏 著
• 出版社 世界图书出版公司
• 出版时间 2012-09
• 版次 1
• ISBN 9787510048029
• 定价 68.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 438页

【内容简介】

　　随机控制也叫试探控制，是最原始的控制方式，是其他一切控制方式的基础。随机控制是完全建立在偶然机遇的基础上，是“试试看”思想在控制活动中的体现。随机控制在成功的同时，常常伴随着失败。这种控制方式有较大的风险，对事关重大的活动，一般不宜采用这种控制方式。《随机控制》（作者雍炯敏）是关于介绍随机控制的英文教材。

【目录】

Preface
Notation
AssumptionIndex
ProblemIndex
Chapter1.BasicStochasticCalculus
1.Probability
1.1.Probabilityspaces
1.2.Randomvariables
1.3.Conditionalexpectation
1.4.Convcrgenceofprobabilities
2.StochasticProcesses
2.1.Generalconsiderations
2.2.Brownianmotions
3.StoppingTimes
4.Martingales
5.ItS'sIntegral
5.1.NondifferentiabilityofBrownianmotion
5.2.DefinitionofItesintegralandbasicproperties
5.3.ItS'sformula
5.4.Martingalerepresentationtheorems
6.StochasticDifferentialEquations
6.1.Strongsolutions
6.2.Weaksolutions
6.3.LinearSDEs
6.4.OthertypesofSDEs
Chapter2.StochasticOptimalControlProblems
1.Introduction
2.DeterministicCasesRevisited
3.ExamplesofStochasticControlProblems
3.1.Productionplanning
3.2.Investmentvs.consumption
3.3.Reinsuranceanddividendmanagement
3.4.Technologydiffusion
3.5.Queueingsystemsinheavytraffic
4.FormulationsofStochasticOptimalControlProblems
4.1.Strongformulation
4.2.Weakformulation
5.ExistenceofOptimalControls
5.1.Adeterministicresult
5.2.Existenceunderstrongformulation
5.3.Existenceunderweakformulation
6.ReachableSetsofStochasticControlSystems
6.1.Nonconvexityofthereachablesets
6.2.Nonclnsenessofthereachablesets
7.OtherStochasticControlModels
7.1.Randomduration
7.2.Optimalstopping
7.3.Singularandimpulsecontrols
7.4.Risk-sensitivecontrols
7.5.Ergodiccontrols
7.6.Partiallyobservablesystems
8.HistoricalRemarks
Chapter3.MaximumPrincipleandStochastic
HamiitonianSystems
1.Introduction
2.TheDeterministicCaseRcvisited
3.StatementoftheStochasticMaximumPrinciple
3.1.Adjointequations
3.2.Themaximumprincipleandstochastic
Hamiltoniansystems
3.3.Aworked-outexample
4.AProofoftheMaximumPrinciple
4.1.Amomentestimate
4.2.Taylorexpansions
4.3.Dualityanalysisandcomplctionofthcproof
5.SufficientConditionsofOptimality
6.ProblemswithStatcConstraints
6.1.Formulationoftheproblemandthemaximumprinciple
6.2.Somepreliminarylemmas
6.3.AproofofTheorem6.1
7.HistoricalRemarks
Chapter4.DynamicProgrammingandHJBEquations
1.Introduction
2.TheDeterministicCascRevisited
3.TheStochasticPrincipleofOptimalityandtheHJBEquation
3.1.Astochasticframeworkfordynamicprogramming
3.2.Principlcofoptimality
3.3.TheHJBcquation
4.OtherPropertiesoftheValueFunction
4.1.Continuousdependenceonparameters
4.2.Semiconcavity
5.Viseo~itySolutions
5.1.Definitions
5.2.Someproperties
6.UniquenessofViscositySolutions
6.1.Auniquenesstheorem
6.2.ProofsofLemmas6.6and6.7
7.HistoricalRcmarks
Chapter5.TheRelationshipBetweentheMaximum
PrincipleandDynamicProgramming
1.Introduction
2.ClassicalHamilton-JacobiTheory
3.RelationshipforDeterministicSystems
3.1.Adjointvariableandvaluefunction:Smoothcase
3.2.Economicinterpretation
3.3.MethodsofcharacteristicsandtheFcynmanKacformula
3.4.Adjointvariableandvaluefunction:Nonsmoothcase
3.5.Vcrificationtheorems
4.RelationshipforStochasticSystems
4.1.Smoothcase
4.2.Nonsmoothcase:Differentialsinthespatialvariable
4.3.Nonsmoothcase:Differentialsinthetimevariable
5.StochasticVcrificationTheorems
5.1.Smoothcase
5.2.Nonsmoothcase
6.OptimalFccdbackControls
7.HistoricalRemarks
Chapter6.LinearQuadraticOptimalControlProblems
1.Introduction
2.TheDeterministicLQProblemsRevisited
2.1.Formulation
2.2.Aminimizationproblemofaquadraticfunctional
2.3.AlinearHamiltoniansystem
2.4.TheRiccatiequationandfeedbackoptimalcontrol
3.FormuLationofStochasticLQProblems
3.1.Statementoftheproblems
3.2.Examples
4.FinitenessandSolvability
5.ANecessaryConditionandaHamiltonianSystem
6.StochasticRiceatiEquations
7.GLobalSolvabilityofStochasticRiccatiEQuations
7.1.Existence:Thcstandardcase
7.2.Existence:ThecaseC=0,S=0,andQ,G>_0
7.3.Existence:Theone-dimensionalcase
8.AMean-variancePortfolioSelectionProblem
9.HistoricalRemarks
Chapter7.BackwardStochasticDifferentialEquations
1.Introduction
2.LinearBackwardStochasticDifferentialEQuations
3.NonlinearBackwardStochasticDifferentialEquations
3.1.BSDEsinfinitedeterministicdurations:Methodof
contractionmapping
3.2.BSDEsinrandomdurations:Methodofcontinuation
4.Feynman-Kac-TypeFormulae
4.1.RepresentationviaSDEs
4.2.RepresentationviaBSDEs
5.Forward-BackwardStochasticDifferentialEquations
5.1.Generalformulationandnonsolvability
5.2.Thefour-stepscheme,aheuristicderivation
5.3.SeveralsolvableclassesofFBSDEs
6.OptionPricingProblems
6.1.EuropeancalloptionsandtheBlack-Scholesformula
6.2.Otheroptions
7.HistoricalRemarks
References
Index