Infinite Dimensional Stochastic Analysis : In Honor of Hui-Hsiung Kuo.
Başlık:
Infinite Dimensional Stochastic Analysis : In Honor of Hui-Hsiung Kuo.
Yazar:
Sengupta, Ambar N.
ISBN:
9789812779557
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (257 pages)
Seri:
Qp-Pq: Quantum Probability and White Noise Analysis ; v.22
Qp-Pq: Quantum Probability and White Noise Analysis
İçerik:
CONTENTS -- 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 operators -- 2.2. 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 product -- 4. 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 Function.
6. 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. Ouerdiane -- 1. 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 -- 3. The Levy Laplacian acting on the Levy distributions -- 4. Extensions of the Levy Laplacian -- 5. Associated infinite dimensional stochastic processes -- 6. A relationship between Kuo's Fourier-Mehler transform and the Levy Laplacian -- Acknowledgments -- References -- The Heat Operator in Infinite Dimensions B. C. Hall -- 1. Introduction -- 2. Gaussian measures -- 3. The Laplacian and the heat operator -- 4. The Segal-Bargmann transform -- 5. "Two wrongs make a right" -- 6. Proof using Hermite polynomials -- 7. The Hermite semigroup and the heat semigroup -- 8. Concluding remarks -- References.
Quantum Stochastic Dilation of Symmetric Covariant Completely Positive Semigroups with Unbounded Generator D. Goswami and K. B. Sinha -- 1. Introduction -- 2. Preliminaries -- 3. Assumptions on the semigroup and its generator -- 4. Evans Hudson type dilation -- 5. Applications and examples -- Acknowledgment -- References -- White Noise Analysis in the Theory of Three-Manifold Quantum Invariants A . Hahn -- 1. Introduction -- 2. The heuristic Chern-Simons path integral in the torus gauge -- 2.1. Chern-Simons models -- 2.2. Some notation related to G and T -- 2.3. Torus gauge fixing applied to Chern-Simons models -- 3. Towards a rigorous realization of the r.h.s. of Eq. (15) -- References -- A New Explicit Formula for the Solution of the Black-Merton- Scholes Equation J. A . Goldstein, R. M. Mininni, and S. Romanelli -- 1. Introduction -- 2. Background -- 3. The Explicit Formula -- References -- Volatility Models of the Yield Curve V. Goodman -- 1. Principal Component Analysis of Forward Interest Rates -- 2. The One-factor Model -- 3. Forward Measure and the One-Factor Model -- 4. The New One-Factor Model -- 5. Multi-factor Models -- Acknowledgment -- References -- Author Index.
Özet:
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, graduate students and applied mathematicians. Sample Chapter(s). Complex White Noise and the Infinite Dimensional Unitary Group (425 KB). Contents: Complex White Noise and the Infinite Dimensional Unitary Group (T Hida); Complex Itô Formulas (M Redfern); White Noise Analysis: Background and a Recent Application (J Becnel & A N Sengupta); Probability Measures with Sub-Additive Principal Szegö-Jacobi Parameters (A Stan); Donsker's Functional Calculus and Related Questions (P-L Chow & J Potthoff); Stochastic Analysis of Tidal Dynamics Equation (U Manna et al.); Adapted Solutions to the Backward Stochastic Navier-Stokes Equations in 3D (P Sundar & H Yin); Spaces of Test and Generalized Functions of Arcsine White Noise Formulas (A Barhoumi et al.); An Infinite Dimensional Fourier-Mehler Transform and the Lévy Laplacian (K Saito & K Sakabe); The Heat Operator in Infinite Dimensions (B C Hall); Quantum Stochastic Dilation of Symmetric Covariant Completely Positive Semigroups with Unbounded Generator (D Goswami & K B Sinha); White Noise Analysis in the Theory of Three-Manifold Quantum Invariants (A Hahn); A New Explicit Formula for the Solution of the Black-Merton-Scholes Equation (J A Goldstein et al.); Volatility Models of the Yield Curve (V Goodman). Readership:
Graduate-level researchers in stochastic analysis, mathematical physics and financial mathematics.
Notlar:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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