SMM Random Fields and Geometry [Adler] 0387481125

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1、SpringerMonographsinMathematicsFromRobertFormyparents,KurtandBertaAdler,whotaughtmethemostimportantlessonofall:Knowfromwhenceyouhavecome,towhereyouaregoing,andbeforeWhomyoumustultimatelyreport.EthicsoftheFathers,Chapter3FromJonathanFormywife,Lee-Ann,anddaughter,Isobel,fortheirtremendoussuppo

2、rtofmyeffortsinwritingthisbookandmyparents,JohnandBrenda,foralloftheirencour-agement.RobertJ.AdlerJonathanE.TaylorRandomFieldsandGeometryWith21IllustrationsRobertAdlerJonathanTaylorFacultyofIndustrialEngineeringDepartmentofStatisticsandManagementStanfordUniversityTechnion–IsraelInstituteofTe

3、chnologySequoiaHallHaifa,32000Stanford,CA94305-4065IsraelU.S.A.MathematicsSubjectClassification(2000):60-02,60Gxx,60G60,53Cxx,53C65LibraryofCongressControlNumber:2007923465ISBN-13:978-0-387-48112-8e-ISBN-13:978-0-387-48116-6Printedonacid-freepaper.©2007SpringerScience+BusinessMediaLLCAllrigh

4、tsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,U.S.A.),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandre

5、trieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubj

6、ecttoproprietaryrights.987654321springer.com(JLS/EB)PrefaceSincetheterm“randomfield’’hasavarietyofdifferentconnotations,rangingfromagriculturetostatisticalmechanics,letusstartbyclarifyingthat,inthisbook,arandomfieldisastochasticprocess,usuallytakingvaluesinaEuclideanspace,anddefinedoveraparamet

7、erspaceofdimensionalityatleast1.Consequently,randomprocessesdefinedoncountableparameterspaceswillnotappearhere.Indeed,evenprocessesonR1willmakeonlyrareappearancesand,fromthepointofviewofthisbook,arealmosttrivial.Theparameterspaceswelikebestaremanifo