SMM Multiparameter Processes An Introduction to Random Fields (Davar Khoshnevisan) 0387954597

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1、SpringerMonographsinMathematicsDavarKhoshnevisanMultiparameterResourcesAnIntroductiontoRandomFieldsDavarKhoshnevisanDepartmentofMathematicsUniversityofUtahSaltLakeCity,Ut84112-0090davar@math.utah.eduWith12illustrations.MathematicsSubjectClassification(2000):60Gxx,60G60LibraryofCongressCat

2、aloging-in-PublicationDataKhoshnevisan,Davar.Multiparameterprocesses:anintroductiontorandomfields/DavarKhoshnevisan.p.cm.—(Springermonographsinmathematics)IncludesbibliographicalreferencesandindexISBN0-387-95459-7(alk.paper)1.Randomfields.I.Title.II.Series.QA274.45.K582002519.2′3—dc212002

3、022927Printedonacid-freepaper.2002Springer-VerlagNewYork,Inc.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(Springer-VerlagNewYork,Inc.,175FifthAvenue,NewYork,NY10010,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholar

4、lyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,eveniftheyarenotidentifiedassuch

5、,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.ManufacturingsupervisedbyJeromeBasma.Camera-readycopypreparedfromtheauthor’sLaTeXfiles.PrintedandboundbyEdwardsBrothers,Inc.,AnnArbor,MI.PrintedintheUnitedStatesofAmerica.987654321ISBN0-387-95459-7SPIN

6、10869448Springer-VerlagNewYorkBerlinHeidelbergAmemberofBertelsmannSpringerScience+BusinessMediaGmbHPrefaceThisbookaimstoconstructageneralframeworkfortheanalysisofalargefamilyofrandomfields,alsoknownasmultiparameterprocesses.TheneedforsuchadevelopmentwaspointedoutinDoob(1990,p.47).Referring

7、tothetheoryofone-parameterstochasticprocesses,Doobwrites:1Ourdefinitionofastochasticprocessishistoricallyconditionedandhasobviousdefects.Inthefirstplacethereisnomathemat-icalreasonforrestrictingTtobeasetofrealnumbers,andinfactinterestingworkhasalreadybeendoneinotherca