LEADER 03304nam 2200505Ia 450 001 9910438160403321 005 20200520144314.0 010 $a3-642-36739-9 024 7 $a10.1007/978-3-642-36739-7 035 $a(OCoLC)846692726 035 $a(MiFhGG)GVRL6YWG 035 $a(CKB)2670000000371292 035 $a(MiAaPQ)EBC1317170 035 $a(EXLCZ)992670000000371292 100 $a20130314d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aFractional fields and applications /$fSerge Cohen and Jacques Istas 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (xii, 270 pages) $cillustrations 225 0 $aMathematiques et applications ;$v73 300 $a"ISSN: 1154-483X." 311 $a3-642-36738-0 320 $aIncludes bibliographical references and index. 327 $aForeword -- Contents -- Introduction -- Preliminaries -- Self-similarity -- Asymptotic self-similarity -- Statistics -- Simulations -- A Appendix -- B Appendix -- References. 330 $aThis book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate. 410 0$aMathematiques & applications ;$v73. 606 $aRandom fields 606 $aRandom walks (Mathematics) 615 0$aRandom fields. 615 0$aRandom walks (Mathematics) 676 $a519.23 700 $aCohen$b Serge$f1964-$01758736 701 $aIstas$b Jacques$f1966-$0287444 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438160403321 996 $aFractional fields and applications$94196988 997 $aUNINA