LEADER 04964nam 2200649Ia 450 001 9910454373803321 005 20200520144314.0 010 $a1-281-93455-0 010 $a9786611934552 010 $a981-279-461-1 035 $a(CKB)1000000000538098 035 $a(EBL)1681709 035 $a(SSID)ssj0000243576 035 $a(PQKBManifestationID)11188243 035 $a(PQKBTitleCode)TC0000243576 035 $a(PQKBWorkID)10160456 035 $a(PQKB)10476813 035 $a(MiAaPQ)EBC1681709 035 $a(WSP)00004445 035 $a(Au-PeEL)EBL1681709 035 $a(CaPaEBR)ebr10255640 035 $a(CaONFJC)MIL193455 035 $a(OCoLC)879025589 035 $a(EXLCZ)991000000000538098 100 $a20000814d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSelected papers of Takeyuki Hida$b[electronic resource] /$fedited by L. Accardi ... [et al.] 210 $aSingapore ;$aRiver Edge, N.J. $cWorld Scientific$dc2001 215 $a1 online resource (496 p.) 300 $aDescription based upon print version of record. 311 $a981-02-4333-2 320 $aIncludes bibliographical references. 327 $aPreface; Contents; I. General Theory of White Noise Punctionals; [1] Analysis of Brownian Functionals; [2] Quadratic Functionals of Brownian Motion; [3] Generalized Brownian Functionals; [4] The Role of Exponential Functions in the Analysis of Generalized Brownian Functionals; [5] Causal Calculus and An Application to Prediction Theory; [6] Generalized Gaussian Measures; [7] The Impact of Classical Functional Analysis on White Noise Calculus; II. Gaussian and Other Processes; [8] Canonical Representations of Gaussian Processes and Their Applications 327 $a[9] Analysis on Hilbert Space with Reproducing Kernel Arising from Multiple Wiener Integral[10] The Square of a Gaussian Markov Process and Nonlinear Prediction; III. Infinite Dimensional Harmonic Analysis and Rotation Group; [11] Sur I'invariance Projective pour les Processus Symetriques Stables; [12] Note on the Infinite Dimensional Laplacian Operator; [13] L'analyse Harmonique sur l'espace des Fonctions Generalisees; [14] Conformal Invariance of White Noise; [15] Transformations for White Noise Functionals; [16] On Projective Invariance of Brownian Motion 327 $a[17] Infinite Dimensional Rotations and Laplacians in Terms of White Noise Calculus[18] Infinite Dimensional Rotation Group and White Noise Analysis; IV. Quantum Theory; [19] On Quantum Theory in Terms of White Noise; [20] White Noise Analysis and Its Applications to Quantum Dynamics; [21] Boson Fock Representations of Stochastic Processes; V. Feynman Integrals and Random Fields; [22] Generalized Brownian Functionals and the Feynman Integral; [23] Dirichlet Forms and White Noise Analysis; [24] Dirichlet Forms in Terms of White Noise Analysis I: Construction and QFT Examples 327 $a[25] Dirichlet Forms in Terms of White Noise Analysis II: Closability and Diffusion ProcessesVI. Variational Calculus and Random Fields; [26] Multidimensional Parameter White Noise and Gaussian Random Fields; [27] A Note on Generalized Gaussian Random Fields; [28] White Noise and Stochastic Variational Calculus for Gaussian Random Fields; [29] Variational Calculus for Gaussian Random Fields; [30] Innovations for Random Fields; VII. Application to Biology; [31] Functional Word in a Protein I Overlapping Words; Comments on [11] [14] [19] [20] and [21]; Comments on [6] [8] [10] [27] and [29] 327 $aComments on [9] [11] [14] [16] [17] and [18]Comments on [1] [2] [4] and [5]; Comments on [12] [13] [16] and [17]; Comments on [15] and [31]; Comments on [26] [28] and [30]; Comments on [20] [22] [23] [24] and [25]; My Mathematical Journey; List of Publications 330 $aThe topics discussed in this book can be classified into three parts:. (i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed. (ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called "generalized white noise functionals", and sometimes "Hida distribution". ( 606 $aStochastic processes 606 $aProbabilities 608 $aElectronic books. 615 0$aStochastic processes. 615 0$aProbabilities. 676 $a519.5 700 $aHida$b Takeyuki$f1927-$047700 701 $aAccardi$b L$g(Luigi),$f1947-$0319693 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454373803321 996 $aSelected papers of Takeyuki Hida$92136883 997 $aUNINA