00844nam0-22002771i-450099000128587040332120170221121851.0000128587FED01000128587(Aleph)000128587FED0100012858720001205d1987----km-y0itay50------baengDiffusion, Markov processes and martingales volume 2Ito CalculusL. C. G. Rogers and David WilliamsChichester [etc.]John Wiley1987v.23 cm2.: Itô calculusRogers,L.C.G.58631Williams,David<1938- >ITUNINARICAUNIMARCBK990001285870403321121-C-8(25848MA1MA1Diffusion, Markov processes and martingales volume 2384867UNINA04618nam 2200649 450 991082535720332120231206212927.01-00-333866-61-003-33866-61-000-79238-287-92982-94-8(CKB)3710000000094832(EBL)3400139(SSID)ssj0001328305(PQKBManifestationID)12414905(PQKBTitleCode)TC0001328305(PQKBWorkID)11283916(PQKB)10764318(Au-PeEL)EBL3400139(CaPaEBR)ebr10852715(OCoLC)878145315(Au-PeEL)EBL7099440(MiAaPQ)EBC3400139(MiAaPQ)EBC7099440(EXLCZ)99371000000009483220230222d2013 uy 0engur|n|---|||||txtccrInternet teletraffic modeling and estimation /Alexandre Barbosa de Lima, Jose Roberto de Almeida AmazonasGistrup, Denmark :River Publishers,[2013]©20131 online resource (186 p.)River Publishers Series in Information Science and TechnologyDescription based upon print version of record.87-92982-10-7 Includes bibliographical references and index.""Cover""; ""Contents""; ""List of Tables""; ""List of Figures""; ""Preface""; ""List of acronyms and symbols""; ""1 Introduction""; ""1.1 Objectives of telecommunications carriers""; ""1.2 Traffic characteristics""; ""1.3 Questions and contributions""; ""1.4 Time series basic concepts""; ""1.4.1 Time series examples""; ""1.4.2 Operators notation""; ""1.4.3 Stochastic processes""; ""1.4.4 Time seriesmodeling""; ""2 The fractal nature of network traffic""; ""2.1 Fractals and self-similarity examples""; ""2.1.1 The Hurst exponent""; ""2.1.2 Samplemean variance""; ""2.2 Long range dependence""""2.2.1 Aggregate process""""2.3 Self-similarity""; ""2.3.1 Exact second order self-similarity""; ""2.3.2 Impulsiveness""; ""2.4 Final remarks: why is the data networks traffic fractal?""; ""3 Modeling of long-range dependent teletraffic""; ""3.1 Classes of modeling""; ""3.1.1 Non-parametric modeling""; ""3.2 Wavelet transform""; ""3.2.1 Multiresolution analysis and the discrete wavelet transform""; ""3.3 ModelMWM""; ""3.4 Parametric modeling""; ""3.4.1 ARFIMAmodel""; ""3.4.2 ARFIMA models prediction - optimum estimation""; ""3.4.3 Formsof prediction""; ""3.4.4 Confidence interval""""3.4.5 ARFIMAprediction""""3.5 Longmemorystatistical tests""; ""3.5.1 R/Sstatistics""; ""3.5.2 GPHtest""; ""3.6 Some H and d estimation methods""; ""3.6.1 R/Sstatistics""; ""3.6.2 Variance plot""; ""3.6.3 Periodogram method""; ""3.6.4 Whittleâ€?s method""; ""3.6.5 Haslett and Rafteryâ€?s MV approximate estimator""; ""3.6.6 Abry andVeitchâ€?swavelet estimator""; ""3.7 Bi-spectrum and linearity test""; ""3.8 KPSS stationarity test""; ""4 State-space modeling""; ""4.1 Introduction""; ""4.2 TARFIMAmodel""; ""4.2.1 Multistep prediction with the Kalman filter""""4.2.2 The prediction power of the TARFIMA model""""4.3 Series exploratory analysis""; ""4.3.1 ARFIMA(0; 0.4; 0) series""; ""4.3.2 MWM series with H = 0.9""; ""4.3.3 Nile river series""; ""4.4 Prediction empirical studywith theTARFIMAmodel""; ""4.4.1 ARFIMA(0, d, 0) series""; ""4.4.2 MWMseries""; ""4.4.3 Nile river series between years 1007 and 1206""; ""4.4.4 Conclusions""; ""5 Modeling of Internet traffic""; ""5.1 Introduction""; ""5.2 Modeling of the UNC02 trace""; ""5.2.1 Exploratory analysis""; ""5.2.2 Long memory local analysis of the UNC02 trace""""5.2.3 Empirical prediction with the TARFIMA model""""6 Conclusions""; ""Bibliography""; ""Index""; ""About the Authors""This book presents a new statespace model for Internet traffic, which is based on a finite-dimensional representation of the Autoregressive Fractionally Integrated Moving Average (ARFIMA) random process. The modeling via Autoregressive (AR) processes is also investigated.TelecommunicationTrafficTelecommunicationTraffic.621.3851Lima Alexandre Barbosa De1625680Amazonas José Roberto de AlmeidaMiAaPQMiAaPQMiAaPQBOOK9910825357203321Internet teletraffic modeling and estimation3961314UNINA