LEADER 03347nam 2200505Ia 450 001 9910735798603321 005 20200520144314.0 010 $a3-319-00936-2 024 7 $a10.1007/978-3-319-00936-0 035 $a(OCoLC)857431888 035 $a(MiFhGG)GVRL6WZK 035 $a(CKB)2670000000533736 035 $a(MiAaPQ)EBC1398619 035 $a(EXLCZ)992670000000533736 100 $a20130813d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis of variations for self-similar processes $ea stochastic calculus approach /$fCiprian A. Tudor 205 $a1st ed. 2013. 210 $aHeidelberg ;$aNew York $cSpringer$dc2013 215 $a1 online resource (xi, 268 pages) 225 1 $aProbability and Its Applications,$x1431-7028 300 $a"ISSN: 1431-7028." 311 $a3-319-00935-4 311 $a3-319-03368-9 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- Part I Examples of Self-Similar Processes -- 1.Fractional Brownian Motion and Related Processes -- 2.Solutions to the Linear Stochastic Heat and Wave Equation -- 3.Non Gaussian Self-Similar Processes -- 4.Multiparameter Gaussian Processes -- Part II Variations of Self-Similar Process: Central and Non-Central Limit Theorems -- 5.First and Second Order Quadratic Variations. Wavelet-Type Variations -- 6.Hermite Variations for Self-Similar Processes -- Appendices: A.Self-Similar Processes with Stationary Increments: Basic Properties -- B.Kolmogorov Continuity Theorem -- C.Multiple Wiener Integrals and Malliavin Derivatives -- References -- Index. 330 $aSelf-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature.  Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of  self-similar processes and their interrrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus. 410 0$aProbability and its applications (Springer-Verlag) 606 $aSelf-similar processes 606 $aStochastic processes 615 0$aSelf-similar processes. 615 0$aStochastic processes. 676 $a519.23 700 $aTudor$b Ciprian A$01752976 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910735798603321 996 $aAnalysis of variations for self-similar processes$94188486 997 $aUNINA