000 04832nam a22006135i 4500
001 978-3-319-71030-3
003 DE-He213
005 20210118124516.0
007 cr nn 008mamaa
008 180105s2017 gw | s |||| 0|eng d
020 _a9783319710303
_9978-3-319-71030-3
024 7 _a10.1007/978-3-319-71030-3
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aKubilius, Kęstutis.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aParameter Estimation in Fractional Diffusion Models
_h[electronic resource] /
_cby Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXIX, 390 p. 17 illus., 2 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,
_x2039-1471 ;
_v8
505 0 _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.
520 _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.
650 0 _aProbabilities.
650 0 _aStatistics .
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aStatistical Theory and Methods.
_0http://scigraph.springernature.com/things/product-market-codes/S11001
700 1 _aMishura, Yuliya.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aRalchenko, Kostiantyn.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319710297
776 0 8 _iPrinted edition:
_z9783319710310
776 0 8 _iPrinted edition:
_z9783319890319
830 0 _aBocconi & Springer Series, Mathematics, Statistics, Finance and Economics,
_x2039-1471 ;
_v8
856 4 0 _uhttps://doi.org/10.1007/978-3-319-71030-3
912 _aZDB-2-SMA
999 _c446571
_d446571
942 _cEB
506 _aAvailable to subscribing member institutions only. Доступно лише організаціям членам підписки.
506 _fOnline access from local network of NaUOA.
506 _fOnline access with authorization at https://link.springer.com/
506 _fОнлайн-доступ з локальної мережі НаУОА.
506 _fОнлайн доступ з авторизацією на https://link.springer.com/