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Selected papers of Takeyuki Hida /
The topics discussed in this book can be classified into three parts: Gaussian processes; white noise analysis; and variational calculus for random fields. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often...
| Call Number: | Libro Electrónico |
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| Main Author: | |
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Singapore ; River Edge, N.J. :
World Scientific,
©2001.
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| Subjects: | |
| Online Access: | Texto completo |
Table of Contents:
- Preface; 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
- [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
- [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
- [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]
- Comments 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