introduction_to_stochastic_processes

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1、IntroductiontoStochasticProcesses-LectureNotes(with33illustrations)GordanŽitkovićDepartmentofMathematicsTheUniversityofTexasatAustinContents1Probabilityreview41.1Randomvariables..........................................41.2Countablesets.................

2、............................51.3Discreterandomvariables.....................................51.4Expectation..............................................71.5Eventsandprobability........................................81.6Dependenceandindependence.......

3、...........................91.7Conditionalprobability.......................................101.8Examples................................................122Mathematicain15min152.1BasicSyntax..............................................152.2NumericalApp

4、roximation.....................................162.3ExpressionManipulation......................................162.4ListsandFunctions.........................................172.5LinearAlgebra............................................192.6PredefinedCo

5、nstants........................................202.7Calculus................................................202.8SolvingEquations..........................................222.9Graphics................................................222.10ProbabilityDist

6、ributionsandSimulation............................232.11HelpCommands...........................................242.12CommonMistakes..........................................253StochasticProcesses263.1Thecanonicalprobabilityspace.........................

7、........273.2ConstructingtheRandomWalk.................................283.3Simulation...............................................293.3.1Randomnumbergeneration...............................293.3.2SimulationofRandomVariables..........................

8、..303.4MonteCarloIntegration......................................334TheSimpleRandomWalk354.1Construction..............................................354.2Themaximum............................................361CONTENTS5Generat