000 03167nam a22004815i 4500
001 978-88-470-2823-4
003 DE-He213
005 20140220083336.0
007 cr nn 008mamaa
008 130125s2012 it | s |||| 0|eng d
020 _a9788847028234
_9978-88-470-2823-4
024 7 _a10.1007/978-88-470-2823-4
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aNourdin, Ivan.
_eauthor.
245 1 0 _aSelected Aspects of Fractional Brownian Motion
_h[electronic resource] /
_cby Ivan Nourdin.
264 1 _aMilano :
_bSpringer Milan :
_bImprint: Springer,
_c2012.
300 _aX, 122 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aB&SS — Bocconi & Springer Series,
_x2039-1471
505 0 _a1. Preliminaries -- 2. Fractional Brownian motion -- 3. Integration with respect to fractional Brownian motion -- 4. Supremum of the fractional Brownian motion -- 5. Malliavin calculus in a nutshell -- 6. Central limit theorem on the Wiener space -- 7. Weak convergence of partial sums of stationary sequences -- 8. Non-commutative fractional Brownian motion.
520 _aFractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.
650 0 _aMathematics.
650 0 _aFinance.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aQuantitative Finance.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9788847028227
830 0 _aB&SS — Bocconi & Springer Series,
_x2039-1471
856 4 0 _uhttp://dx.doi.org/10.1007/978-88-470-2823-4
912 _aZDB-2-SMA
999 _c104205
_d104205