这本书就是矿主推荐的那本，今天整理资料发现了，拿出来与大家分享，市面上有卖纸质版的，看不惯电子书的童鞋可以去买本（我就是这样 ）

想做练习题的童鞋建议去市面上买第六版，因为第六版配习题参考答案


Book Description

This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications.


TableofContents

1.Introduction :::::::::::::::::::::::::::::::::::::::::::::: 1
1.1StochasticAnalogsofClassicalDi®erentialEquations.......1
1.2FilteringProblems......................................2
1.3StochasticApproachtoDeterministicBoundaryValueProb-
lems..................................................2
1.4OptimalStopping......................................3
1.5StochasticControl......................................4
1.6MathematicalFinance..................................4
2.SomeMathematicalPreliminaries :::::::::::::::::::::::: 7
2.1ProbabilitySpaces,RandomVariablesandStochasticProcesses7
2.2AnImportantExample:BrownianMotion.................11
Exercises..................................................14
3.It^oIntegrals :::::::::::::::::::::::::::::::::::::::::::::: 21
3.1ConstructionoftheIt^oIntegral..........................21
3.2SomepropertiesoftheIt^ointegral........................30
3.3ExtensionsoftheIt^ointegral............................34
Exercises..................................................37
4.TheIt^oFormulaandtheMartingaleRepresentationTheo-
rem::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43
4.1The1-dimensionalIt^oformula...........................43
4.2TheMulti-dimensionalIt^oFormula.......................48
4.3TheMartingaleRepresentationTheorem..................49
Exercises..................................................54
5.StochasticDi®erentialEquations ::::::::::::::::::::::::: 61
5.1ExamplesandSomeSolutionMethods....................61
5.2AnExistenceandUniquenessResult......................66
5.3WeakandStrongSolutions..............................70
Exercises..................................................
6.TheFilteringProblem :::::::::::::::::::::::::::::::::::: 81
6.1Introduction...........................................81
6.2The1-DimensionalLinearFilteringProblem...............83
6.3TheMultidimensionalLinearFilteringProblem............102
Exercises..................................................103
7.Di®usions:BasicProperties ::::::::::::::::::::::::::::::: 109
7.1TheMarkovProperty...................................109
7.2TheStrongMarkovProperty............................112
7.3TheGeneratorofanIt^oDi®usion........................117
7.4TheDynkinFormula....................................120
7.5TheCharacteristicOperator.............................122
Exercises..................................................124
8.OtherTopicsinDi®usionTheory ::::::::::::::::::::::::: 133
8.1Kolmogorov'sBackwardEquation.TheResolvent..........133
8.2TheFeynman-KacFormula.Killing.......................137
8.3TheMartingaleProblem................................140
8.4WhenisanIt^oProcessaDi®usion?.......................142
8.5RandomTimeChange..................................147
8.6TheGirsanovTheorem..................................153
Exercises..................................................160
9.ApplicationstoBoundaryValueProblems :::::::::::::::: 167
9.1TheCombinedDirichlet-PoissonProblem.Uniqueness.......167
9.2TheDirichletProblem.RegularPoints....................169
9.3ThePoissonProblem...................................181
Exercises..................................................188
10.ApplicationtoOptimalStopping ::::::::::::::::::::::::: 195
10.1TheTime-HomogeneousCase............................195
10.2TheTime-InhomogeneousCase..........................207
10.3OptimalStoppingProblemsInvolvinganIntegral...........212
10.4ConnectionwithVariationalInequalities...................214
Exercises..................................................218
11.ApplicationtoStochasticControl ::::::::::::::::::::::::: 225
11.1StatementoftheProblem...............................225
11.2TheHamilton-Jacobi-BellmanEquation...................227
11.3Stochasticcontrolproblemswithterminalconditions........241
Exercises..................................................243TableofContentsXIX
12.ApplicationtoMathematicalFinance ::::::::::::::::::::: 249
12.1Market,portfolioandarbitrage...........................249
12.2AttainabilityandCompleteness..........................259
12.3OptionPricing.........................................267
Exercises..................................................288
AppendixA:NormalRandomVariables :::::::::::::::::::::: 295
AppendixB:ConditionalExpectation :::::::::::::::::::::::: 299
AppendixC:UniformIntegrabilityandMartingaleConver-gence ::::::::::::::::::::::::::::::::::::::::::::::::::::: 301
AppendixD:AnApproximationResult ::::::::::::::::::::::: 305
SolutionsandAdditionalHintstoSomeoftheExercises :::::: 309
References :::::::::::::::::::::::::::::::::::::::::::::::::::: 317
ListofFrequentlyUsedNotationandSymbols ::::::::::::::: 325
Index ::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 329