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Infinite Dimensional Stochastic Analysis : In Honor of Hui-Hsiung Kuo.
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 pa...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific Publishing Company,
2008.
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| Colección: | QP-PQ, quantum probability and white noise analysis.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 2.1. 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.
- 3. 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.
- 5.3. 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.
- Spaces 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.