02393nam 2200469 450 991083023650332120200528201531.51-119-47677-11-119-61033-81-119-61034-6(CKB)4100000007934813(MiAaPQ)EBC5748885(CaSebORM)9781786302601(EXLCZ)99410000000793481320190427d2019 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierFractional brownian motion approximations and projections /Oksana Banna, [and three others]1st editionHoboken, New Jersey :ISTE :Wiley,2019.1 online resource (293 pages)1-78630-260-8 This 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.Brownian motion processesMartingales (Mathematics)Brownian motion processes.Martingales (Mathematics)530.475Banna Oksana1638535Mishura YuliyaRalchenko KostiantynShklyar SergiyMiAaPQMiAaPQMiAaPQBOOK9910830236503321Fractional brownian motion3981034UNINA