Probability_random_processes_and_ergodic_properties

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1、Probability,RandomProcesses,andErgodicPropertiesiiProbability,RandomProcesses,andErgodicPropertiesRobertM.GrayInformationSystemsLaboratoryElectricalEngineeringDepartmentStanfordUniversitySpringer-VerlagNewYorkivc1987bySpringerVerlag.Revised2001and2006–200

2、7byRobertM.Gray.vThisbookisaffectionatelydedicatedtothememoryofElizabethDuboisJordanGray1906–1998R.Adm.AugustineHeardGray,U.S.N.1888-1981SaraJeanDuboisandWilliam“OldBilly”Gray1750-1825viContentsContentsviiPrefaceix1ProbabilityandRandomProcesses11.1Introduc

3、tion.........................................11.2ProbabilitySpacesandRandomVariables........................11.3RandomProcessesandDynamicalSystems.......................61.4Distributions........................................81.5Extension................

4、..........................131.6Isomorphism........................................192Standardalphabets212.1ExtensionofProbabilityMeasures............................212.2StandardSpaces......................................222.3Somepropertiesofstandardspac

5、es............................262.4Simplestandardspaces...................................292.5MetricSpaces........................................312.6ExtensioninStandardSpaces...............................362.7TheKolmogorovExtensionTheorem.............

6、..............372.8ExtensionWithoutaBasis................................383BorelSpacesandPolishalphabets453.1BorelSpaces........................................453.2PolishSpaces........................................483.3PolishSchemes...................

7、....................544Averages614.1Introduction.........................................614.2DiscreteMeasurements...................................614.3Quantization........................................644.4Expectation.................................

8、........674.5TimeAverages.......................................774.6ConvergenceofRandomVariables............................804.7StationaryAverages....................................87viiviiiCONTENTS5ConditionalPr