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1、RANDOMPROCESSESBYEXAMPLE8883_9789814522281_tp.indd114/1/144:27pmMay2,201314:6BC:8831-ProbabilityandStatisticalTheoryPST˙wsThispageintentionallyleftblankRANDOMPROCESSESBYEXAMPLEMikhailLifshitsSt.PetersburgStateUniversity,Russia&Link?pingUniversity,SwedenW
2、orldScientificNEWJERSEY?LONDON?SINGAPORE?BEIJING?SHANGHAI?HONGKONG?TAIPEI?CHENNAI8883_9789814522281_tp.indd214/1/144:27pmPublishedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UK
3、office:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.RANDOMPROCESSESBYEXAMPLECopyright?2014byWorldScientificPublishingCo.Pte.Ltd.Allrightsreserved.Thisboo
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6、PrefaceThestoryoftheselecturesissomewhatunusual.FewyearsagoIwasreadingaresearchmanuscriptbyI.KajandM.S.Taqqu[49]thathandledthelimitbehaviorof“teletra?csystems”.Clearly,thiswasadeepandimportantpieceofmodernmathematicsbrilliantlyrepresentingawaveofinterest
7、tothesubject,seee.g.[8,10],[13,14,48],[69,87],[70,71,108],tomentionjustafew.Whatapparentlypassedlessappreciated,wasatremendousvalueofteletra?cmodelsforteachingandlearning.Inasimpleandintuitivelytrivialmodel,aminortuningoffewparametersleadstodi?erentworkl
8、oadregimes–Wienerprocess,fractionalBrownianmotion,stableL′evyprocess,aswellastosomelesscommonlyknownones,calledbyKajandTaqqu“Telecomprocesses”.Simplicityofthedependencemechanismusedinthemodelenablestogetaclearunderstanding
