03655nam 2200613 a 450 991045780760332120200520144314.01-280-37753-49786613555441981-4366-37-4(CKB)2550000000079298(EBL)840718(SSID)ssj0000645935(PQKBManifestationID)12266759(PQKBTitleCode)TC0000645935(PQKBWorkID)10684684(PQKB)11561601(MiAaPQ)EBC840718(WSP)00008251(Au-PeEL)EBL840718(CaPaEBR)ebr10524571(CaONFJC)MIL355544(OCoLC)877767936(EXLCZ)99255000000007929820120207d2012 uy 0engur|n|---|||||txtccrGeneralized functionals of Brownian motion and their applications[electronic resource] nonlinear functionals of fundamental stochastic processes /N.U. AhmedSingapore ;Hackensack World Scientificc20121 online resource (314 p.)Description based upon print version of record.981-4366-36-6 Includes bibliographical references (p. 291-296) and index.Preface; Contents; 1. Background Material; 1.1 Introduction; 1.2 Wiener Process and Wiener Measure; 1.3 Stochastic Differential Equations in Rd; 1.4 Stochastic Differential Equations in H; 1.4.1 Measure Solutions; 1.5 Nonlinear Filtering; 1.5.1 Finite Dimensional Filtering; 1.5.2 Infinite Dimensional Filtering; 1.6 Elements of Vector Measures; 1.7 Some Problems for Exercise; 2. Regular Functionals of Brownian Motion; 2.1 Introduction; 2.2 Functionals of Scalar Brownian Motion; 2.3 Functionals of Vector Brownian Motion; 2.4 Functionals of Gaussian Random Field (GRF)5.6 Some Problems for Exercise6. Lp-Based Generalized Functionals of White Noise III; 6.1 Introduction; 6.2 Homogeneous Functionals of Degree n; 6.3 Nonhomogeneous Functionals; 6.4 Weighted Generalized Functionals; 6.5 Some Examples Related to Section 6.4; 6.6 Generalized Functionals of Random Fields Applied; 6.7 ̃ Fq-Valued Vector Measures with Application; 6.8 Some Problems for Exercise; 7. Wp,m-Based Generalized Functionals of White Noise IV; 7.1 Introduction; 7.2 Homogeneous Functionals; 7.3 Nonhomogeneous Functionals; 7.4 Inductive and Projective Limits8.7.2 Smoothness under H ̈ormander's ConditionsThis invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph developBrownian motion processesStochastic processesElectronic books.Brownian motion processes.Stochastic processes.515.3Ahmed N. U(Nasir Uddin)848296MiAaPQMiAaPQMiAaPQBOOK9910457807603321Generalized functionals of Brownian motion and their applications2118887UNINA