000			03688nam a22005415i 4500
001			978-3-642-36739-7
003			DE-He213
005			20140220082905.0
007			cr nn 008mamaa
008			130531s2013 gw | s |||| 0|eng d
020			_a9783642367397 _9978-3-642-36739-7
024	7		_a10.1007/978-3-642-36739-7 _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		_aCohen, Serge. _eauthor.
245	1	0	_aFractional Fields and Applications _h[electronic resource] / _cby Serge Cohen, Jacques Istas.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2013.
300			_aXII, 270 p. 27 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aMathématiques et Applications, _x1154-483X ; _v73
505	0		_aForeword -- Contents -- Introduction -- Preliminaries -- Self-similarity -- Asymptotic self-similarity -- Statistics -- Simulations -- A Appendix -- B Appendix -- References.
520			_aThis book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.
650		0	_aMathematics.
650		0	_aDistribution (Probability theory).
650		0	_aPhysics.
650		0	_aMathematical statistics.
650		0	_aEngineering.
650	1	4	_aMathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aStatistical Theory and Methods.
650	2	4	_aComplexity.
650	2	4	_aStatistical Physics, Dynamical Systems and Complexity.
700	1		_aIstas, Jacques. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642367380
830		0	_aMathématiques et Applications, _x1154-483X ; _v73
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-36739-7
912			_aZDB-2-SMA
999			_c97944 _d97944