LEADER 04542nam 2200781Ia 450 001 9910969630003321 005 20200520144314.0 010 $a9786612087592 010 $a9781282087590 010 $a1282087592 010 $a9781400825103 010 $a1400825105 010 $a9781400814244 010 $a1400814243 024 7 $a10.1515/9781400825103 035 $a(CKB)111056486507912 035 $a(EBL)445477 035 $a(OCoLC)609842105 035 $a(SSID)ssj0000243851 035 $a(PQKBManifestationID)11190666 035 $a(PQKBTitleCode)TC0000243851 035 $a(PQKBWorkID)10181402 035 $a(PQKB)11167507 035 $a(DE-B1597)446357 035 $a(OCoLC)979578170 035 $a(DE-B1597)9781400825103 035 $a(Au-PeEL)EBL445477 035 $a(CaPaEBR)ebr10284069 035 $a(CaONFJC)MIL208759 035 $a(PPN)170237176 035 $a(FR-PaCSA)45001617 035 $a(MiAaPQ)EBC445477 035 $a(Perlego)734172 035 $a(FRCYB45001617)45001617 035 $a(EXLCZ)99111056486507912 100 $a20020611d2002 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aSelfsimilar processes /$fPaul Embrechts and Makoto Maejima 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$dc2002 215 $a1 online resource (123 p.) 225 1 $aPrinceton series in applied mathematics 300 $aDescription based upon print version of record. 311 08$a9780691096278 311 08$a0691096279 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tChapter 1. Introduction --$tChapter 2. Some Historical Background --$tChapter 3. Self similar Processes with Stationary Increments --$tChapter 4. Fractional Brownian Motion --$tChapter 5. Self similar Processes with Independent Increments --$tChapter 6. Sample Path Properties of Self similar Stable Processes with Stationary Increments --$tChapter 7. Simulation of Self similar Processes --$tChapter 8. Statistical Estimation --$tChapter 9. Extensions --$tReferences --$tIndex 330 $aThe modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration. Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity. 410 0$aPrinceton series in applied mathematics. 606 $aDistribution (Probability theory) 606 $aSelf-similar processes 615 0$aDistribution (Probability theory) 615 0$aSelf-similar processes. 676 $a519.2/4 686 $aSK 820$2rvk 700 $aEmbrechts$b Paul$f1953-$028027 701 $aMaejima$b Makoto$0726746 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910969630003321 996 $aSelfsimilar processes$91422107 997 $aUNINA