04542nam 2200781Ia 450 991096963000332120200520144314.0978661208759297812820875901282087592978140082510314008251059781400814244140081424310.1515/9781400825103(CKB)111056486507912(EBL)445477(OCoLC)609842105(SSID)ssj0000243851(PQKBManifestationID)11190666(PQKBTitleCode)TC0000243851(PQKBWorkID)10181402(PQKB)11167507(DE-B1597)446357(OCoLC)979578170(DE-B1597)9781400825103(Au-PeEL)EBL445477(CaPaEBR)ebr10284069(CaONFJC)MIL208759(PPN)170237176(FR-PaCSA)45001617(MiAaPQ)EBC445477(Perlego)734172(FRCYB45001617)45001617(EXLCZ)9911105648650791220020611d2002 uy 0engurnn#---|u||utxtccrSelfsimilar processes /Paul Embrechts and Makoto MaejimaCourse BookPrinceton, N.J. Princeton University Pressc20021 online resource (123 p.)Princeton series in applied mathematicsDescription based upon print version of record.9780691096278 0691096279 Includes bibliographical references and index.Front matter --Contents --Chapter 1. Introduction --Chapter 2. Some Historical Background --Chapter 3. Self similar Processes with Stationary Increments --Chapter 4. Fractional Brownian Motion --Chapter 5. Self similar Processes with Independent Increments --Chapter 6. Sample Path Properties of Self similar Stable Processes with Stationary Increments --Chapter 7. Simulation of Self similar Processes --Chapter 8. Statistical Estimation --Chapter 9. Extensions --References --IndexThe modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.Princeton series in applied mathematics.Distribution (Probability theory)Self-similar processesDistribution (Probability theory)Self-similar processes.519.2/4SK 820rvkEmbrechts Paul1953-28027Maejima Makoto726746MiAaPQMiAaPQMiAaPQBOOK9910969630003321Selfsimilar processes1422107UNINA