随机微分方程

图书标准信息

• 作者 BerntφKsendal 著
• 出版社 世界图书出版公司
• 出版时间 2006-05
• 版次 1
• ISBN 9787506273084
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 365页

【内容简介】

　　随机微分方程在数学以外的许多领域有着广泛的应用，它对数学领域中的许多分支起着有效的联结作用。本书是《Universitext》丛书之一，是一部理想的研究生教材。我们曾影印出版了第2版和第4版，第6版与第4版相比，内容做了较大的修改和补充，增加了90页的篇幅(近1／3内容)，包括鞅表示论、变分不等式和随机控制等内容，书后附有部分习题解答和提示。

【目录】

Introduction
1.1StochasticAnalogsofClassicalDifferentialEquations
1.2FilteringProblems
1.3StochasticApproachtoDeterministicBoundaryValueProblems
1.4OptimalStopping
1.5StochasticControl
1.6MathematicalFinance
SomeMathematicalPreliminaries
2.1ProbabilitySpaces，RandomVariablesandStochasticProcesses
2.2AnImportantExample：BrownianMotion
Exercises
ItoIntegrals
3.1ConstructionoftheIt5Integral
3.2SomepropertiesoftheIt5integral
3.3ExtensionsoftheItointegral
Exercises
TheItoFormulaandtheMartingaleRepresentation
Theorem
4.1The1-dimensionalIt5formula
4.2TheMulti-dimensionalIt5Formula
4.3TheMartingaleRepresentationTheorem
Exercises
StochasticDifferentialEquations
5.1ExamplesandSomeSolutionMethods
5.2AnExistenceandUniquenessResult
5.3WeakandStrongSolutions
Exercises
6TheFilteringProblem
6.1Introduction
6.2The1-DimensionalLinearFilteringProblem
6.3TheMultidimensionalLinearFilteringProblem
Exercises
7Diffusions：BasicProperties
7.1TheMarkovProperty
7.2TheStrongMarkovProperty
7.3TheGeneratorofanIt5Diffusion
7.4TheDynkinFormula
7.5TheCharacteristicOperator
Exercises
8OtherTopicsinDiffusionTheory
8.1KolmogorovsBackwardEquation.TheResolvent
8.2TheFeynman-KacFormula.Killing
8.3TheMartingaleProblem
8.4WhenisanIt5ProcessaDiffusion?
8.5RandomTimeChange
8.6TheGirsanovTheorem
Exercises
9ApplicationstoBoundaryValueProblems
9.1TheCombinedDirichlet-PoissonProblem.Uniqueness
9.2TheDirichletProblem.RegularPoints
9.3ThePoissonProblem
Exercises
10ApplicationtoOptimalStopping
10.1TheTime-HomogeneousCase
10.2TheTime-InhomogeneousCase
10.3OptimalStoppingProblemsInvolvinganIntegral
10.4ConnectionwithVariationalInequalities
Exercises
11ApplicationtoStochasticControl
11.1StatementoftheProblem
11.2TheHa.milton-Jacobi-BellmanEquation
11.3Stochasticcontrolproblemswithterminalconditions
Exercises
12ApplicationtoMathematicalFinance
12.1Market，portfolioandarbitrage
12.2AttainabilityandCompleteness
12.3OptionPricing
Exercises
AppendixA：NormalRandomVariables
AppendixB：ConditionalExpectation
AppendixC：UniformIntegrabilityandMartingale
Convergence
AppendixD：AnApproximationResult
SolutionsandAdditionalHintstoSomeoftheExercises..
References
ListofFrequentlyUsedNotationandSymbols
Index