theory of stochastic processes

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1、36-754,AdvancedProbabilityIIorAlmostNoneoftheTheoryofStochasticProcessesCosmaShaliziSpring2007ContentsTableofContentsiComprehensiveListofDefinitions,Lemmas,Propositions,Theo-rems,Corollaries,ExamplesandExercisesxxiiiPreface1IStochasticProcessesinGeneral21Basic

2、s31.1So,WhatIsaStochasticProcess?.................31.2RandomFunctions..........................51.3Exercises...............................72BuildingProcesses152.1Finite-DimensionalDistributions..................152.2ConsistencyandExtension...................

3、..163BuildingProcessesbyConditioning213.1ProbabilityKernels..........................213.2ExtensionviaRecursiveConditioning...............223.3Exercises...............................25IIOne-ParameterProcessesinGeneral264One-ParameterProcesses274.1One-Paramet

4、erProcesses......................274.2OperatorRepresentationsofOne-ParameterProcesses......314.3Exercises...............................315StationaryProcesses345.1KindsofStationarity.........................34iCONTENTSii5.2StrictlyStationaryProcessesandMeasur

5、e-PreservingTransfor-mations................................355.3Exercises...............................376RandomTimes386.1RemindersaboutFiltrationsandStoppingTimes.........386.2WaitingTimes............................396.3Kac’sRecurrenceTheorem.............

6、........416.4Exercises...............................457Continuity467.1KindsofContinuityforProcesses..................467.2WhyContinuityIsanIssue.....................487.3SeparableRandomFunctions....................507.4Exercises..............................

7、.518MoreonContinuity528.1SeparableVersions..........................528.2MeasurableVersions.........................578.3CadlagVersions............................588.4ContinuousModifications......................59IIIMarkovProcesses609MarkovProcesses619.1TheC

8、orrectLineontheMarkovProperty.............619.2TransitionProbabilityKernels...................629.3TheMarkovPropertyUnderMultipleFiltrations.........659.4Exercises........................