资源描述：
《probability, random processes and ergodic properties - gray》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、Probability,RandomProcesses,andErgodicPropertiesNovember3,2001iiProbability,RandomProcesses,andErgodicPropertiesRobertM.GrayInformationSystemsLaboratoryDepartmentofElectricalEngineeringStanfordUniversityiv°c1987bySpringerVerlag,2001revisionbyRobertM.Gray
2、.vThisbookisa®ectionatelydedicatedtoElizabethDuboisJordanGrayandtothememoryofR.Adm.AugustineHeardGray,U.S.N.1888-1981SaraJeanDuboisandWilliamBilly"Gray1750-1825viPrefaceHistoryandGoalsThisbookhasbeenwrittenforseveralreasons,notallofwhichareacademic.This
3、materialwasformanyyearsthe¯rsthalfofabookinprogressoninformationandergodictheory.Theintentwasandistoprovideareasonablyself-containedadvancedtreatmentofmeasuretheory,probabilitytheory,andthetheoryofdiscretetimerandomprocesseswithanemphasisongeneralalphabe
4、tsandonergodicandstationarypropertiesofrandomprocessesthatmightbeneitherergodicnorstationary.Theintendedaudiencewasmathematicallyinclinedengineeringgraduatestudentsandvisitingscholarswhohadnothadformalcoursesinmeasuretheoreticprobability.Muchofthemateria
5、lisfamiliarstu®formathematicians,butmanyofthetopicsandresultshavenotpreviouslyappearedinbooks.Theoriginalprojectgrewtoolargeandthe¯rstpartcontainedmuchthatwouldlikelyboremathematiciansanddiscouragethemfromthesecondpart.HenceI¯nallyfollowedasuggestiontose
6、paratethematerialandsplittheprojectintwo.Theoriginaljusti¯cationforthepresentmanuscriptwasthepragmaticonethatitwouldbeashametowasteallthee®ortthusfarexpended.Amoreidealisticmotivationwasthatthepresentationhadmeritas¯llingaunique,albeitsmall,holeinthelite
7、rature.Personalexperienceindicatesthattheintendedaudiencerarelyhasthetimetotakeacompletecourseinmeasureandprobabilitytheoryinamathematicsorstatisticsdepartment,atleastnotbeforetheyneedsomeofthematerialintheirresearch.Inaddition,manyoftheexistingmathemati
8、caltextsonthesubjectarehardforthisaudiencetofollow,andtheemphasisisnotwellmatchedtoengineeringapplications.AnotableexceptionisAsh'sexcellenttext[1],whichwaslikelyin°uencedbyhisoriginaltrainingasanelectricalengineer.Still,e
