03460nam 2200577 a 450 991048345830332120200520144314.03-540-75873-910.1007/978-3-540-75873-0(CKB)1000000000437243(SSID)ssj0000320218(PQKBManifestationID)11274552(PQKBTitleCode)TC0000320218(PQKBWorkID)10343644(PQKB)10713216(DE-He213)978-3-540-75873-0(MiAaPQ)EBC3068754(PPN)125217803(EXLCZ)99100000000043724320071010d2008 uy 0engurnn|008mamaatxtccrStochastic calculus for fractional Brownian motion and related processes /Yuliya S. Mishura1st ed. 2008.Berlin Springer-Verlagc20081 online resource (XVIII, 398 p.) Lecture notes in mathematics,0075-8434 ;1929Bibliographic Level Mode of Issuance: Monograph3-540-75872-0 Includes bibliographical references (p. [369]-389) and index.Wiener integration with respect to fractional Brownian motion -- Stochastic integration with respect to fBm and related topics -- Stochastic differential equations involving fractional Brownian motion -- Filtering in systems with fractional Brownian noise -- Financial applications of fractional Brownian motion -- Tactical inference with fractional Brownian motion -- A: Mandelbrot-van Ness representation : some related calculations -- Approximation of beta integrals and estimation of kernels.The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0<H<1/2 of Hurst index, the conditions of existence and uniqueness of solutions to SDE involving additive Wiener integrals, and of solutions of the mixed Brownian—fractional Brownian SDE. The author develops optimal filtering of mixed models including linear case, and studies financial applications and statistical inference with hypotheses testing and parameter estimation. She proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.Lecture notes in mathematics (Springer-Verlag) ;1929.Fractional Brownian motion and related processesBrownian motion processesMathematical modelsStochastic analysisBrownian motion processesMathematical models.Stochastic analysis.530.4/75015192260G1560G4460G6060H0560H0760H1060H4091B2491B28mscMishura IUliia S313976MiAaPQMiAaPQMiAaPQBOOK9910483458303321Stochastic calculus for fractional Brownian motion and related processes230627UNINA