LEADER 04040nam 22005775 450 001 9910255456703321 005 20250315152907.0 010 $a9783319710303 010 $a3319710303 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 $aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,$x2039-148X ;$v8 311 08$a9783319710297 311 08$a331971029X 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,$x2039-148X ;$v8 606 $aProbabilities 606 $aStatistics 606 $aProbability Theory 606 $aStatistical Theory and Methods 615 0$aProbabilities. 615 0$aStatistics. 615 14$aProbability Theory. 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 LEADER 00979nam0 22002651i 450 001 UON00051009 005 20231205102225.930 100 $a20020107d1979 |0itac50 ba 101 $arus 102 $aSU 105 $a|||| 1|||| 200 1 $aNastol'nye poiskovye sistemy$fB. V. Jakusin 210 $aMoskva$cIzdatel'stvo Nauka$d1979 215 $a110 p.$d21 cm 606 $aLinguistica$3UONC002524$2FI 620 $aRU$dMoskva$3UONL003152 686 $aIG XVII$cINTERESSI GENERALI - PEDAGOGIA$2A 700 1$aJAKUSIN$bBoris Vladimorovic$3UONV032254$0651106 712 $aAkademija Nauk SSSR$3UONV247334$4650 801 $aIT$bSOL$c20250523$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00051009 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI IG XVII 002 $eSI SA 55046 5 002 996 $aNastol'nye poiskovye sistemy$91144602 997 $aUNIOR