LEADER 02427nam 2200481 450 001 9910555094403321 005 20200528201531.5 010 $a1-119-47677-1 010 $a1-119-61033-8 010 $a1-119-61034-6 035 $a(CKB)4100000007934813 035 $a(MiAaPQ)EBC5748885 035 $a(CaSebORM)9781786302601 035 $a(EXLCZ)994100000007934813 100 $a20190427d2019 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFractional brownian motion $eapproximations and projections /$fOksana Banna, [and three others] 205 $a1st edition 210 1$aHoboken, New Jersey :$cISTE :$cWiley,$d2019. 215 $a1 online resource (293 pages) 311 $a1-78630-260-8 330 $aThis monograph studies the relationships between fractional Brownian motion (fBm) and other processes of more simple form. In particular, this book solves the problem of the projection of fBm onto the space of Gaussian martingales that can be represented as Wiener integrals with respect to a Wiener process. It is proved that there exists a unique martingale closest to fBm in the uniform integral norm. Numerical results concerning the approximation problem are given. The upper bounds of distances from fBm to the different subspaces of Gaussian martingales are evaluated and the numerical calculations are involved. The approximations of fBm by a uniformly convergent series of Lebesgue integrals, semimartingales and absolutely continuous processes are presented. As auxiliary but interesting results, the bounds from below and from above for the coefficient appearing in the representation of fBm via the Wiener process are established and some new inequalities for Gamma functions, and even for trigonometric functions, are obtained. 606 $aBrownian motion processes 606 $aMartingales (Mathematics) 608 $aElectronic books. 615 0$aBrownian motion processes. 615 0$aMartingales (Mathematics) 676 $a530.475 700 $aBanna$b Oksana$01218777 702 $aMishura$b Yuliya 702 $aRalchenko$b Kostiantyn 702 $aShklyar$b Sergiy 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910555094403321 996 $aFractional brownian motion$92818370 997 $aUNINA