LEADER 05633nam 2200709 a 450 001 9910453201803321 005 20200520144314.0 010 $a1-281-93809-2 010 $a9786611938093 010 $a981-277-955-8 035 $a(CKB)1000000000538166 035 $a(EBL)1679419 035 $a(OCoLC)879023624 035 $a(SSID)ssj0000178851 035 $a(PQKBManifestationID)11189181 035 $a(PQKBTitleCode)TC0000178851 035 $a(PQKBWorkID)10229836 035 $a(PQKB)11205019 035 $a(MiAaPQ)EBC1679419 035 $a(WSP)00001865 035 $a(Au-PeEL)EBL1679419 035 $a(CaPaEBR)ebr10255385 035 $a(CaONFJC)MIL193809 035 $a(EXLCZ)991000000000538166 100 $a20071218d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aInfinite dimensional stochastic analysis$b[electronic resource] $ein honor of Hui-Hsiung Kuo /$feditors, Ambar N. Sengupta, P. Sundar 210 $aNew Jersey $cWorld Scientific$dc2008 215 $a1 online resource (257 p.) 225 1 $aQP-PQ, quantum probability and white noise analysis ;$vv. 22 300 $aDescription based upon print version of record. 311 $a981-277-954-X 320 $aIncludes bibliographical references and index. 327 $aCONTENTS; Preface; Complex White Noise and the Infinite Dimensional Unitary Group T. Hida; 1. Introduction; 2. Complex white noise; 3. Infinite dimensional unitary group; 4. Subgroups of U(Ee); References; Complex Ito Formulas M. Redfern; 1. Introduction; 2. Background and Notation; 3. Complex White Noise Analysis; 4. Calculus of (Dc*)-Valued Processes; 5. Real Case; References; White Noise Analysis: Background and a Recent Application J. Becnel and A . N. Sengupta; 1. Introduction; 2. Background: The Schwartz Space as a Nuclear Space 327 $a2.1. Hermite polynomials, creation and annihilation operators2.2. The Schwartz space as a nuclear space; 2.3. The abstract formulation; 2.4. Gaussian measure in infinite dimensions; 3. White Noise Distribution Theory; 3.1. Wiener-Ito isomorphism; 3.2. Properties of test functions; 3.3. The Segal-Bargmann transform; 3.3.1. The S-transform over subspaces; 4. Application to Quantum Computing; 4.1. Quantum algorithms; 4.2. Hidden subspace algorithm; Acknowledgment; References; Probability Measures with Sub-Additive Principal Szego-Jacobi Parameters A. Stan; 1. Introduction; 2. Background 327 $a3. Wick product4. Random variables with sub-additive w-parameters; References; Donsker's Functional Calculus and Related Questions P.-L. Chow and J. Potthoff; 1. Introduction; 2. Donsker's Calculus; 3. Tools from White Noise Analysis and Malliavin Calclus; 3.1. Chaos Decomposition; 3.2. S-Transform; 3.3. Smooth and Generalized Random Variables; 3.4. Differential Operators; 3.5. Characterization Theorem and Wick Product; 4. Fourier-Wiener Transform; 5. Independence and Ito Calculus; 5.1. Independence of Generalized Random Variables; 5.2. Ito Calculus for Generalized Stochastic Processes 327 $a5.3. Donsker's Delta Function6. Towards Donsker's Calculus; References; Stochastic Analysis of Tidal Dynamics Equation U. Manna, J. L. Menaldi, and S. S. Sritharan; 1. Introduction; 2. Tidal Dynamics: The Model; 3. Deterministic Setting: Global Monotonicity and Solvability; 4. Stochastic Tide Equation; Acknowledgments; References; Adapted Solutions to the Backward Stochastic Navier-Stokes Equations in 3D P. Sundar and H. Yin; 1. Introduction; 2. Preliminaries; 3. A Priori Estimates; 4. Existence of Solutions; 5. Uniqueness of Solutions; References 327 $aSpaces of Test and Generalized Functions of Arcsine White Noise Formulas A . Barhoumi, A . Riahi, and H. Ouerdiane1. Introduction; 2. Arcsine White Noise Space; 2.1. Arcsine space in one dimension; 2.2. Construction of the arcsine white noise space; 3. Arcsine Test and Generalized Functions Spaces; 4. Characterization Theorems; 4.1. The S-transform; 4.2. Characterization of test and generalized functions; References; An Infinite Dimensional Fourier-Mehler Transform and the Levy Laplacian K. Saito and K. Sakabe; 1. Introduction; 2. A compensated Levy process and the Levy distributions 327 $a3. The Levy Laplacian acting on the Levy distributions 330 $a This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduat 410 0$aQP-PQ ;$vv. 22. 410 0$aQP-PQ, quantum probability and white noise analysis ;$vv. 22. 606 $aWhite noise theory 606 $aStochastic analysis 608 $aElectronic books. 615 0$aWhite noise theory. 615 0$aStochastic analysis. 676 $a519.2/2 701 $aKuo$b Hui-Hsiung$f1941-$012283 701 $aSengupta$b Ambar$f1963-$0150693 701 $aSundar$b P$g(Padmanabhan)$0903218 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453201803321 996 $aInfinite dimensional stochastic analysis$92019051 997 $aUNINA