随机微分方程
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15
3.8折
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39
九品
库存2件
作者BerntφKsendal 著
出版社世界图书出版公司
出版时间2006-05
版次1
装帧平装
货号2-3
上书时间2024-07-17
商品详情
- 品相描述:九品
图书标准信息
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作者
BerntφKsendal 著
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出版社
世界图书出版公司
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出版时间
2006-05
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版次
1
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ISBN
9787506273084
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定价
39.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
365页
- 【内容简介】
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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】
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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
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