Preface
PrefacetotheFirstEdition
AbbreviationsandSymbols
1.Preliminaries
1.1NotationsAndConventions
1.2Measurability,LpSpacesAndMonotoneClassTheorems
1.3FunctionsofBoundedVariationAndStieltjesIntegrals
1.4ProbabilitySpace,RandomVariables,Filtration
1.5Convergence,Conditioning
1.6StochasticProcesses
1.7OptionalTimes
1.8TwoCanonicalProcesses
1.9Martingales
1.10LocalMartingales
1.11Exercises
2.DefinitionofTheStochasticIntegral
2.1Introduction
2.2PredictableSetsAndProcesses
2.3StochasticIntervals
2.4MeasureonThePredictableSets
2.5DefinitionofTheStochasticIntegral
2.6ExtensionToLocalIntegratorsAndIntegrands
2.7SubstitutionFormula
2.8ASufficientConditionforExtendabilityofHz
2.9Exercises
3.ExtensionofThePredictableIntegrands
3.1Introduction
3.2RelationshipBetweenP,O,AndAdaptedProcesses
3.3ExtensionofTheIntegrands
3.4AHistoricalNote
3.5Exercises
4.QuadraticVariationProcess
4.1Introduction
4.2DefinitionAndCharacterizationofQuadraticVariation
4.3PropertiesofQuadraticVariationForAnL2-Wartingale
4.4DirectDefinitionofΜM
4.5Decompositionof(M)2
4.6ALimitTheorem
4.7Exercises
5.TheItoFormula
5.1Introduction
5.2One-DimensionalIt5Formula
5.3MutualVariationProcess
5.4Multi-DimensionalIt5Formula
5.5Exercises
……
6.ApplicationsofTheItoFormula
7.LocalTimeandTanaka'sFormula
8.ReflectedBrownianMotions
9.GeneralizedFroFormula,ChangeofTimeandMeasure
10.StochasticDifferentialEquations