000			03495nam a22004937a 4500
001			sulb-eb0023329
003			BD-SySUS
005			20160413122345.0
007			cr nn 008mamaa
008			130805s2013 gw | s |||| 0|eng d
020			_a9783319009360 _9978-3-319-00936-0
024	7		_a10.1007/978-3-319-00936-0 _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		_aTudor, Ciprian. _eauthor.
245	1	0	_aAnalysis of Variations for Self-similar Processes _h[electronic resource] : _bA Stochastic Calculus Approach / _cby Ciprian Tudor.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2013.
300			_aXI, 268 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProbability and Its Applications, _x1431-7028
505	0		_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.
520			_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.
650		0	_aMathematics.
650		0	_aProbabilities.
650		0	_aStatistics.
650	1	4	_aMathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aStatistics, general.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319009353
830		0	_aProbability and Its Applications, _x1431-7028
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-319-00936-0
912			_aZDB-2-SMA
942			_2Dewey Decimal Classification _ceBooks
999			_c45421 _d45421