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gray r.m. probability, random processes, and ergodic properties (springer, 1987, revised 2001)(218s)

gray r.m. probability, random processes, and ergodic properties (springer, 1987, revised 2001)(218s)

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页数：218页

时间：2018-07-27

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1、Probability,RandomProcesses,andErgodicPropertiesNovember3,2001iiProbability,RandomProcesses,andErgodicPropertiesRobertM.GrayInformationSystemsLaboratoryDepartmentofElectricalEngineeringStanfordUniversityiv°c1987bySpringerVerlag,2001revisionbyRobertM.Gray.vThisbookisa®ecti

2、onatelydedicatedtoElizabethDuboisJordanGrayandtothememoryofR.Adm.AugustineHeardGray,U.S.N.1888-1981SaraJeanDuboisandWilliamBilly"Gray1750-1825viPrefaceHistoryandGoalsThisbookhasbeenwrittenforseveralreasons,notallofwhichareacademic.Thismaterialwasformanyyearsthe¯rsthalfof

3、abookinprogressoninformationandergodictheory.Theintentwasandistoprovideareasonablyself-containedadvancedtreatmentofmeasuretheory,probabilitytheory,andthetheoryofdiscretetimerandomprocesseswithanemphasisongeneralalphabetsandonergodicandstationarypropertiesofrandomprocesses

4、thatmightbeneitherergodicnorstationary.Theintendedaudiencewasmathematicallyinclinedengineeringgraduatestudentsandvisitingscholarswhohadnothadformalcoursesinmeasuretheoreticprobability.Muchofthematerialisfamiliarstu®formathematicians,butmanyofthetopicsandresultshavenotprev

5、iouslyappearedinbooks.Theoriginalprojectgrewtoolargeandthe¯rstpartcontainedmuchthatwouldlikelyboremathematiciansanddiscouragethemfromthesecondpart.HenceI¯nallyfollowedasuggestiontoseparatethematerialandsplittheprojectintwo.Theoriginaljusti¯cationforthepresentmanuscriptwas

6、thepragmaticonethatitwouldbeashametowasteallthee®ortthusfarexpended.Amoreidealisticmotivationwasthatthepresentationhadmeritas¯llingaunique,albeitsmall,holeintheliterature.Personalexperienceindicatesthattheintendedaudiencerarelyhasthetimetotakeacompletecourseinmeasureandpr

7、obabilitytheoryinamathematicsorstatisticsdepartment,atleastnotbeforetheyneedsomeofthematerialintheirresearch.Inaddition,manyoftheexistingmathematicaltextsonthesubjectarehardforthisaudiencetofollow,andtheemphasisisnotwellmatchedtoengineeringapplications.Anotableexceptionis

8、Ash'sexcellenttext[1],whichwaslikelyin°uencedbyhisoriginaltrainingasanelectricalengineer.Still,e

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