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1、RANDOMPROCESSESBYEXAMPLE8883_9789814522281_tp.indd114/1/144:27pmMay2,201314:6BC:8831-ProbabilityandStatisticalTheoryPST˙wsThispageintentionallyleftblankRANDOMPROCESSESBYEXAMPLEMikhailLifshitsSt.PetersburgStateUniversity,Russia&LinköpingUniversity,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
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5、pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.ISBN978-981-4522-28-1PrintedinSingaporeDecember24,201311:23BC:8883-RandomProcessesbyExampleDG˙ws
6、PrefaceThestoryoftheselecturesissomewhatunusual.FewyearsagoIwasreadingaresearchmanuscriptbyI.KajandM.S.Taqqu[49]thathandledthelimitbehaviorof“teletrafficsystems”.Clearly,thiswasadeepandimportantpieceofmodernmathematicsbrilliantlyrepresentingawaveofinterest
7、tothesubject,seee.g.[8,10],[13,14,48],[69,87],[70,71,108],tomentionjustafew.Whatapparentlypassedlessappreciated,wasatremendousvalueofteletrafficmodelsforteachingandlearning.Inasimpleandintuitivelytrivialmodel,aminortuningoffewparametersleadstodifferentworkl
8、oadregimes–Wienerprocess,fractionalBrownianmotion,stableL´evyprocess,aswellastosomelesscommonlyknownones,calledbyKajandTaqqu“Telecomprocesses”.Simplicityofthedependencemechanismusedinthemodelenablestogetaclearunderstanding
