LEADER 03655nam 2200613 a 450 001 9910457807603321 005 20200520144314.0 010 $a1-280-37753-4 010 $a9786613555441 010 $a981-4366-37-4 035 $a(CKB)2550000000079298 035 $a(EBL)840718 035 $a(SSID)ssj0000645935 035 $a(PQKBManifestationID)12266759 035 $a(PQKBTitleCode)TC0000645935 035 $a(PQKBWorkID)10684684 035 $a(PQKB)11561601 035 $a(MiAaPQ)EBC840718 035 $a(WSP)00008251 035 $a(Au-PeEL)EBL840718 035 $a(CaPaEBR)ebr10524571 035 $a(CaONFJC)MIL355544 035 $a(OCoLC)877767936 035 $a(EXLCZ)992550000000079298 100 $a20120207d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeneralized functionals of Brownian motion and their applications$b[electronic resource] $enonlinear functionals of fundamental stochastic processes /$fN.U. Ahmed 210 $aSingapore ;$aHackensack $cWorld Scientific$dc2012 215 $a1 online resource (314 p.) 300 $aDescription based upon print version of record. 311 $a981-4366-36-6 320 $aIncludes bibliographical references (p. 291-296) and index. 327 $aPreface; 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) 327 $a5.6 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 Limits 327 $a8.7.2 Smoothness under H ?ormander's Conditions 330 $aThis 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 develop 606 $aBrownian motion processes 606 $aStochastic processes 608 $aElectronic books. 615 0$aBrownian motion processes. 615 0$aStochastic processes. 676 $a515.3 700 $aAhmed$b N. U$g(Nasir Uddin)$0848296 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910457807603321 996 $aGeneralized functionals of Brownian motion and their applications$92118887 997 $aUNINA