{"product_id":"9781786302601","title":"Fractional Brownian Motion Approximations and Projections","description":"\u003ch1\u003eFractional Brownian Motion\u003c\/h1\u003e\u003ch2\u003eApproximations and Projections\u003c\/h2\u003e\u003ch3\u003eOksana Banna | Yuliya Mishura | Kostiantyn Ralchenko | Sergiy Shklyar\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Probability \u0026amp; Statistics \/ General\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cp\u003eThis 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.\u003cbr\u003e \u003cbr\u003e 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. \u003c\/p\u003e\u003c\/div\u003e\u003cdiv\u003e \u003cp\u003e\u003cb\u003eOksana Banna\u003c\/b\u003e is Assistant Professor at the Department of Economic Cybernetics at Taras Shevchenko National University of Kyiv (KNU) in Ukraine.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eYuliya Mishura\u003c\/b\u003e is Full Professor and Head of the Department of Probability, Statistics and Actuarial Mathematics at KNU.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eKostiantyn Ralchenko\u003c\/b\u003e is Associate Professor at the Department of Probability, Statistics and Actuarial Mathematics at KNU.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSergiy Shklyar\u003c\/b\u003e is Senior Researcher at the Department of Probability, Statistics and Actuarial Mathematics at KNU.\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e30 April 2019\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eWiley\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eWiley-ISTE\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9781786302601\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003eHardback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e288\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eWeight (oz): \u003c\/td\u003e\n\u003ctd\u003e20.0\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":44382055760012,"sku":"9781786302601","price":160.16,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781786302601.jpg?v=1780239712","url":"https:\/\/lateknightbooks.com\/products\/9781786302601","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}