LEADER 04191nam 22005535 450 001 9910255456703321 005 20200629182111.0 010 $a3-319-71030-3 024 7 $a10.1007/978-3-319-71030-3 035 $a(CKB)3790000000544837 035 $a(DE-He213)978-3-319-71030-3 035 $a(MiAaPQ)EBC5215418 035 $a(PPN)223956619 035 $a(EXLCZ)993790000000544837 100 $a20180105d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aParameter Estimation in Fractional Diffusion Models /$fby K?stutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIX, 390 p. 17 illus., 2 illus. in color.) 225 1 $aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,$x2039-1471 ;$v8 311 $a3-319-71029-X 320 $aIncludes bibliographical references and index. 327 $a1 Description and properties of the basic stochastic models -- 2 The Hurst index estimators for a fractional Brownian motion -- 3 Estimation of the Hurst index from the solution of a stochastic differential equation -- 4 Parameter estimation in the mixed models via power variations -- 5 Drift parameter estimation in diffusion and fractional diffusion models -- 6 The extended Orey index for Gaussian processes -- 7 Appendix A: Selected facts from mathematical and functional analysis -- 8 Appendix B: Selected facts from probability, stochastic processes and stochastic calculus. 330 $aThis book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is ?white,? i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics. 410 0$aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,$x2039-1471 ;$v8 606 $aProbabilities 606 $aStatistics  606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001 615 0$aProbabilities. 615 0$aStatistics . 615 14$aProbability Theory and Stochastic Processes. 615 24$aStatistical Theory and Methods. 676 $a530.475 700 $aKubilius$b K?stutis$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767645 702 $aMishura$b Yuliya$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRalchenko$b Kostiantyn$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910255456703321 996 $aParameter Estimation in Fractional Diffusion Models$91924976 997 $aUNINA