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Infinite dimensional stochastic analysis [[electronic resource] ] : in honor of Hui-Hsiung Kuo / / editors, Ambar N. Sengupta, P. Sundar
| Infinite dimensional stochastic analysis [[electronic resource] ] : in honor of Hui-Hsiung Kuo / / editors, Ambar N. Sengupta, P. Sundar |
| Pubbl/distr/stampa | New Jersey, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (257 p.) |
| Disciplina | 519.2/2 |
| Altri autori (Persone) |
KuoHui-Hsiung <1941->
SenguptaAmbar <1963-> SundarP (Padmanabhan) |
| Collana | QP-PQ, quantum probability and white noise analysis |
| Soggetto topico |
White noise theory
Stochastic analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-93809-2
9786611938093 981-277-955-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 3. The Levy Laplacian acting on the Levy distributions |
| Record Nr. | UNINA-9910453201803321 |
| New Jersey, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Infinite dimensional stochastic analysis [[electronic resource] ] : in honor of Hui-Hsiung Kuo / / editors, Ambar N. Sengupta, P. Sundar
| Infinite dimensional stochastic analysis [[electronic resource] ] : in honor of Hui-Hsiung Kuo / / editors, Ambar N. Sengupta, P. Sundar |
| Pubbl/distr/stampa | New Jersey, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (257 p.) |
| Disciplina | 519.2/2 |
| Altri autori (Persone) |
KuoHui-Hsiung <1941->
SenguptaAmbar <1963-> SundarP (Padmanabhan) |
| Collana | QP-PQ, quantum probability and white noise analysis |
| Soggetto topico |
White noise theory
Stochastic analysis |
| ISBN |
1-281-93809-2
9786611938093 981-277-955-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 3. The Levy Laplacian acting on the Levy distributions |
| Record Nr. | UNINA-9910782272003321 |
| New Jersey, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Infinite dimensional stochastic analysis : in honor of Hui-Hsiung Kuo / / editors, Ambar N. Sengupta, P. Sundar
| Infinite dimensional stochastic analysis : in honor of Hui-Hsiung Kuo / / editors, Ambar N. Sengupta, P. Sundar |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | New Jersey, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (257 p.) |
| Disciplina | 519.2/2 |
| Altri autori (Persone) |
KuoHui-Hsiung <1941->
SenguptaAmbar <1963-> SundarP (Padmanabhan) |
| Collana | QP-PQ, quantum probability and white noise analysis |
| Soggetto topico |
White noise theory
Stochastic analysis |
| ISBN |
1-281-93809-2
9786611938093 981-277-955-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 3. The Levy Laplacian acting on the Levy distributions |
| Record Nr. | UNINA-9910810337403321 |
| New Jersey, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to Hida distributions [[electronic resource] /] / Si Si
| Introduction to Hida distributions [[electronic resource] /] / Si Si |
| Autore | Si Si |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (268 p.) |
| Disciplina | 519.22 |
| Soggetto topico |
White noise theory
Stochastic analysis Stochastic differential equations |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-36188-3
9786613555250 981-283-689-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Preliminaries and Discrete Parameter White Noise; 1.1 Preliminaries; 1.2 Discrete parameter white noise; 1.3 Invariance of the measure μ; 1.4 Harmonic analysis arising from O(E) on the space of functionals of Y = {Y (n)}; 1.5 Quadratic forms; 1.6 Differential operators and related operators; 1.7 Probability distributions and Bochner-Minlos theorem; 2. Continuous Parameter White Noise; 2.1 Gaussian system; 2.2 Continuous parameter white noise; 2.3 Characteristic functional and Bochner-Minlos theorem; 2.4 Passage from discrete to continuous
2.5 Stationary generalized stochastic processes3. White Noise Functionals; 3.1 In line with standard analysis; 3.2 White noise functionals; 3.3 Infinite dimensional spaces spanned by generalized linear functionals of white noise; 3.4 Some of the details of quadratic functionals of white noise; 3.5 The T -transform and the S-transform; 3.6 White noise (t) related to δ-function; 3.7 Infinite dimensional space generated by Hermite polynomials in (t)'s of higher degree; 3.8 Generalized white noise functionals; 3.9 Approximation to Hida distributions 3.10 Renormalization in Hida distribution theory4. White Noise Analysis; 4.1 Operators acting on (L2)-; 4.2 Application to stochastic differential equation; 4.3 Differential calculus and Laplacian operators; 4.4 Infinite dimensional rotation group O(E); 4.5 Addenda; 5. Stochastic Integral; 5.1 Introduction; 5.2 Wiener integrals and multiple Wiener integrals; 5.3 The Ito integral; 5.4 Hitsuda-Skorokhod integrals; 5.5 Levy's stochastic integral; 5.6 Addendum : Path integrals; 6. Gaussian and Poisson Noises; 6.1 Poisson noise and its probability distribution 6.2 Comparison between the Gaussian white noise and the Poisson noise, with the help of characterization of measures6.3 Symmetric group in Poisson noise analysis; 6.4 Spaces of quadratic Hida distributions and their dualities; 7. Multiple Markov Properties of Generalized Gaussian Processes and Generalizations; 7.1 A brief discussion on canonical representation theory for Gaussian processes and multiple Markov property; 7.2 Duality for multiple Markov Gaussian processes in the restricted sense; 7.3 Uniformly multiple Markov processes 9.3 Stable distribution |
| Record Nr. | UNINA-9910457274603321 |
Si Si
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to Hida distributions [[electronic resource] /] / Si Si
| Introduction to Hida distributions [[electronic resource] /] / Si Si |
| Autore | Si Si |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (268 p.) |
| Disciplina | 519.22 |
| Soggetto topico |
White noise theory
Stochastic analysis Stochastic differential equations |
| ISBN |
1-280-36188-3
9786613555250 981-283-689-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Preliminaries and Discrete Parameter White Noise; 1.1 Preliminaries; 1.2 Discrete parameter white noise; 1.3 Invariance of the measure μ; 1.4 Harmonic analysis arising from O(E) on the space of functionals of Y = {Y (n)}; 1.5 Quadratic forms; 1.6 Differential operators and related operators; 1.7 Probability distributions and Bochner-Minlos theorem; 2. Continuous Parameter White Noise; 2.1 Gaussian system; 2.2 Continuous parameter white noise; 2.3 Characteristic functional and Bochner-Minlos theorem; 2.4 Passage from discrete to continuous
2.5 Stationary generalized stochastic processes3. White Noise Functionals; 3.1 In line with standard analysis; 3.2 White noise functionals; 3.3 Infinite dimensional spaces spanned by generalized linear functionals of white noise; 3.4 Some of the details of quadratic functionals of white noise; 3.5 The T -transform and the S-transform; 3.6 White noise (t) related to δ-function; 3.7 Infinite dimensional space generated by Hermite polynomials in (t)'s of higher degree; 3.8 Generalized white noise functionals; 3.9 Approximation to Hida distributions 3.10 Renormalization in Hida distribution theory4. White Noise Analysis; 4.1 Operators acting on (L2)-; 4.2 Application to stochastic differential equation; 4.3 Differential calculus and Laplacian operators; 4.4 Infinite dimensional rotation group O(E); 4.5 Addenda; 5. Stochastic Integral; 5.1 Introduction; 5.2 Wiener integrals and multiple Wiener integrals; 5.3 The Ito integral; 5.4 Hitsuda-Skorokhod integrals; 5.5 Levy's stochastic integral; 5.6 Addendum : Path integrals; 6. Gaussian and Poisson Noises; 6.1 Poisson noise and its probability distribution 6.2 Comparison between the Gaussian white noise and the Poisson noise, with the help of characterization of measures6.3 Symmetric group in Poisson noise analysis; 6.4 Spaces of quadratic Hida distributions and their dualities; 7. Multiple Markov Properties of Generalized Gaussian Processes and Generalizations; 7.1 A brief discussion on canonical representation theory for Gaussian processes and multiple Markov property; 7.2 Duality for multiple Markov Gaussian processes in the restricted sense; 7.3 Uniformly multiple Markov processes 9.3 Stable distribution |
| Record Nr. | UNINA-9910778818303321 |
|
Si Si
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to Hida distributions / / Si Si
| Introduction to Hida distributions / / Si Si |
| Autore | Si Si |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2012 |
| Descrizione fisica | 1 online resource (268 p.) |
| Disciplina | 519.22 |
| Soggetto topico |
White noise theory
Stochastic analysis Stochastic differential equations |
| ISBN |
1-280-36188-3
9786613555250 981-283-689-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Preliminaries and Discrete Parameter White Noise; 1.1 Preliminaries; 1.2 Discrete parameter white noise; 1.3 Invariance of the measure μ; 1.4 Harmonic analysis arising from O(E) on the space of functionals of Y = {Y (n)}; 1.5 Quadratic forms; 1.6 Differential operators and related operators; 1.7 Probability distributions and Bochner-Minlos theorem; 2. Continuous Parameter White Noise; 2.1 Gaussian system; 2.2 Continuous parameter white noise; 2.3 Characteristic functional and Bochner-Minlos theorem; 2.4 Passage from discrete to continuous
2.5 Stationary generalized stochastic processes3. White Noise Functionals; 3.1 In line with standard analysis; 3.2 White noise functionals; 3.3 Infinite dimensional spaces spanned by generalized linear functionals of white noise; 3.4 Some of the details of quadratic functionals of white noise; 3.5 The T -transform and the S-transform; 3.6 White noise (t) related to δ-function; 3.7 Infinite dimensional space generated by Hermite polynomials in (t)'s of higher degree; 3.8 Generalized white noise functionals; 3.9 Approximation to Hida distributions 3.10 Renormalization in Hida distribution theory4. White Noise Analysis; 4.1 Operators acting on (L2)-; 4.2 Application to stochastic differential equation; 4.3 Differential calculus and Laplacian operators; 4.4 Infinite dimensional rotation group O(E); 4.5 Addenda; 5. Stochastic Integral; 5.1 Introduction; 5.2 Wiener integrals and multiple Wiener integrals; 5.3 The Ito integral; 5.4 Hitsuda-Skorokhod integrals; 5.5 Levy's stochastic integral; 5.6 Addendum : Path integrals; 6. Gaussian and Poisson Noises; 6.1 Poisson noise and its probability distribution 6.2 Comparison between the Gaussian white noise and the Poisson noise, with the help of characterization of measures6.3 Symmetric group in Poisson noise analysis; 6.4 Spaces of quadratic Hida distributions and their dualities; 7. Multiple Markov Properties of Generalized Gaussian Processes and Generalizations; 7.1 A brief discussion on canonical representation theory for Gaussian processes and multiple Markov property; 7.2 Duality for multiple Markov Gaussian processes in the restricted sense; 7.3 Uniformly multiple Markov processes 9.3 Stable distribution |
| Record Nr. | UNINA-9910821509903321 |
|
Si Si
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures on white noise functionals [[electronic resource] /] / T. Hida, Si Si
| Lectures on white noise functionals [[electronic resource] /] / T. Hida, Si Si |
| Autore | Hida Takeyuki <1927-> |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 519.2/2 |
| Altri autori (Persone) | SiSi |
| Soggetto topico |
White noise theory
Gaussian processes |
| Soggetto genere / forma | Electronic books. |
| ISBN | 981-281-204-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Preliminaries; 1.2 Our idea of establishing white noise analysis; 1.3 A brief synopsis of the book; 1.4 Some general background; 1.4.1 Characteristics of white noise analysis; 2. Generalized white noise functionals; 2.1 Brownian motion and Poisson process; elemental stochastic processes; 2.2 Comparison between Brownian motion and Poisson process; 2.3 The Bochner-Minlos theorem; 2.4 Observation of white noise through the L evy's construction of Brownian motion; 2.5 Spaces (L2), F and F arising from white noise; 2.6 Generalized white noise functionals
A. Use of the Sobolev space structureB. An analogue of the Schwartz space.; 2.7 Creation and annihilation operators; 2.8 Examples; 2.9 Addenda; A.1. The Gauss transform, the S-transform and applications; A.2. The Karhunen-Lo eve expansion; A.3. Reproducing kernel Hilbert space; 3. Elemental random variables and Gaussian processes; 3.1 Elemental noises; I. The first method of stochastic integral.; II. The second method of stochastic integral.; 3.2 Canonical representation of a Gaussian process; 3.3 Multiple Markov Gaussian processes; 3.4 Fractional Brownian motion 3.5 Stationarity of fractional Brownian motion3.6 Fractional order differential operator in connection with L evy's Brownian motion; 3.7 Gaussian random fields; 4. Linear processes and linear fields; 4.1 Gaussian systems; 4.2 Poisson systems; 4.3 Linear functionals of Poisson noise; 4.4 Linear processes; 4.5 L evy field and generalized L evy field; 4.6 Gaussian elemental noises; 5. Harmonic analysis arising from infinite dimensional rotation group; 5.1 Introduction; 5.2 Infinite dimensional rotation group O(E); 5.3 Harmonic analysis; 5.4 Addenda to the diagram 5.5 The L evy group, the Windmill subgroup and the sign-changing subgroup of O(E)5.6 Classification of rotations in O(E); 5.7 Unitary representation of the infinite dimensional rotation group O(E); 5.8 Laplacian; 6. Complex white noise and infinite dimensional unitary group; 6.1 Why complex?; 6.2 Some background; 6.3 Subgroups of U(Ec); 6.4 Applications; I. Symmetry of the heat equation and the Schr odinger equation.; II. Analysis on half plane of E; 7. Characterization of Poisson noise; 7.1 Preliminaries; 7.2 A characteristic of Poisson noise; 7.3 A characterization of Poisson noise 7.4 Comparison of two noises Gaussian and Poisson; 7.5 Poisson noise functionals; 8. Innovation theory; 8.1 A short history of innovation theory; 8.2 Definitions and examples; 8.3 Innovations in the weak sense; 8.4 Some other concrete examples; 9. Variational calculus for random fields and operator fields; 9.1 Introduction; 9.2 Stochastic variational equations; 9.3 Illustrative examples; 9.4 Integrals of operators; 9.4.1 Operators of linear form; 9.4.2 Operators of quadratic forms of the creation and the annihilation operators; 9.4.3 Polynomials in R; of degree 2 10. Four notable roads to quantum dynamics |
| Record Nr. | UNINA-9910455529303321 |
|
Hida Takeyuki <1927->
|
||
| Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures on white noise functionals [[electronic resource] /] / T. Hida, Si Si
| Lectures on white noise functionals [[electronic resource] /] / T. Hida, Si Si |
| Autore | Hida Takeyuki <1927-2017.> |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 519.2/2 |
| Altri autori (Persone) | SiSi |
| Soggetto topico |
White noise theory
Gaussian processes |
| ISBN | 981-281-204-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Preliminaries; 1.2 Our idea of establishing white noise analysis; 1.3 A brief synopsis of the book; 1.4 Some general background; 1.4.1 Characteristics of white noise analysis; 2. Generalized white noise functionals; 2.1 Brownian motion and Poisson process; elemental stochastic processes; 2.2 Comparison between Brownian motion and Poisson process; 2.3 The Bochner-Minlos theorem; 2.4 Observation of white noise through the L evy's construction of Brownian motion; 2.5 Spaces (L2), F and F arising from white noise; 2.6 Generalized white noise functionals
A. Use of the Sobolev space structureB. An analogue of the Schwartz space.; 2.7 Creation and annihilation operators; 2.8 Examples; 2.9 Addenda; A.1. The Gauss transform, the S-transform and applications; A.2. The Karhunen-Lo eve expansion; A.3. Reproducing kernel Hilbert space; 3. Elemental random variables and Gaussian processes; 3.1 Elemental noises; I. The first method of stochastic integral.; II. The second method of stochastic integral.; 3.2 Canonical representation of a Gaussian process; 3.3 Multiple Markov Gaussian processes; 3.4 Fractional Brownian motion 3.5 Stationarity of fractional Brownian motion3.6 Fractional order differential operator in connection with L evy's Brownian motion; 3.7 Gaussian random fields; 4. Linear processes and linear fields; 4.1 Gaussian systems; 4.2 Poisson systems; 4.3 Linear functionals of Poisson noise; 4.4 Linear processes; 4.5 L evy field and generalized L evy field; 4.6 Gaussian elemental noises; 5. Harmonic analysis arising from infinite dimensional rotation group; 5.1 Introduction; 5.2 Infinite dimensional rotation group O(E); 5.3 Harmonic analysis; 5.4 Addenda to the diagram 5.5 The L evy group, the Windmill subgroup and the sign-changing subgroup of O(E)5.6 Classification of rotations in O(E); 5.7 Unitary representation of the infinite dimensional rotation group O(E); 5.8 Laplacian; 6. Complex white noise and infinite dimensional unitary group; 6.1 Why complex?; 6.2 Some background; 6.3 Subgroups of U(Ec); 6.4 Applications; I. Symmetry of the heat equation and the Schr odinger equation.; II. Analysis on half plane of E; 7. Characterization of Poisson noise; 7.1 Preliminaries; 7.2 A characteristic of Poisson noise; 7.3 A characterization of Poisson noise 7.4 Comparison of two noises Gaussian and Poisson; 7.5 Poisson noise functionals; 8. Innovation theory; 8.1 A short history of innovation theory; 8.2 Definitions and examples; 8.3 Innovations in the weak sense; 8.4 Some other concrete examples; 9. Variational calculus for random fields and operator fields; 9.1 Introduction; 9.2 Stochastic variational equations; 9.3 Illustrative examples; 9.4 Integrals of operators; 9.4.1 Operators of linear form; 9.4.2 Operators of quadratic forms of the creation and the annihilation operators; 9.4.3 Polynomials in R; of degree 2 10. Four notable roads to quantum dynamics |
| Record Nr. | UNINA-9910777934303321 |
|
Hida Takeyuki <1927-2017.>
|
||
| Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Lectures on white noise functionals / / T. Hida, Si Si
| Lectures on white noise functionals / / T. Hida, Si Si |
| Autore | Hida Takeyuki <1927-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2008 |
| Descrizione fisica | 1 online resource (280 p.) |
| Disciplina | 519.2/2 |
| Altri autori (Persone) | SiSi |
| Soggetto topico |
White noise theory
Gaussian processes |
| ISBN | 981-281-204-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Preliminaries; 1.2 Our idea of establishing white noise analysis; 1.3 A brief synopsis of the book; 1.4 Some general background; 1.4.1 Characteristics of white noise analysis; 2. Generalized white noise functionals; 2.1 Brownian motion and Poisson process; elemental stochastic processes; 2.2 Comparison between Brownian motion and Poisson process; 2.3 The Bochner-Minlos theorem; 2.4 Observation of white noise through the L evy's construction of Brownian motion; 2.5 Spaces (L2), F and F arising from white noise; 2.6 Generalized white noise functionals
A. Use of the Sobolev space structureB. An analogue of the Schwartz space.; 2.7 Creation and annihilation operators; 2.8 Examples; 2.9 Addenda; A.1. The Gauss transform, the S-transform and applications; A.2. The Karhunen-Lo eve expansion; A.3. Reproducing kernel Hilbert space; 3. Elemental random variables and Gaussian processes; 3.1 Elemental noises; I. The first method of stochastic integral.; II. The second method of stochastic integral.; 3.2 Canonical representation of a Gaussian process; 3.3 Multiple Markov Gaussian processes; 3.4 Fractional Brownian motion 3.5 Stationarity of fractional Brownian motion3.6 Fractional order differential operator in connection with L evy's Brownian motion; 3.7 Gaussian random fields; 4. Linear processes and linear fields; 4.1 Gaussian systems; 4.2 Poisson systems; 4.3 Linear functionals of Poisson noise; 4.4 Linear processes; 4.5 L evy field and generalized L evy field; 4.6 Gaussian elemental noises; 5. Harmonic analysis arising from infinite dimensional rotation group; 5.1 Introduction; 5.2 Infinite dimensional rotation group O(E); 5.3 Harmonic analysis; 5.4 Addenda to the diagram 5.5 The L evy group, the Windmill subgroup and the sign-changing subgroup of O(E)5.6 Classification of rotations in O(E); 5.7 Unitary representation of the infinite dimensional rotation group O(E); 5.8 Laplacian; 6. Complex white noise and infinite dimensional unitary group; 6.1 Why complex?; 6.2 Some background; 6.3 Subgroups of U(Ec); 6.4 Applications; I. Symmetry of the heat equation and the Schr odinger equation.; II. Analysis on half plane of E; 7. Characterization of Poisson noise; 7.1 Preliminaries; 7.2 A characteristic of Poisson noise; 7.3 A characterization of Poisson noise 7.4 Comparison of two noises Gaussian and Poisson; 7.5 Poisson noise functionals; 8. Innovation theory; 8.1 A short history of innovation theory; 8.2 Definitions and examples; 8.3 Innovations in the weak sense; 8.4 Some other concrete examples; 9. Variational calculus for random fields and operator fields; 9.1 Introduction; 9.2 Stochastic variational equations; 9.3 Illustrative examples; 9.4 Integrals of operators; 9.4.1 Operators of linear form; 9.4.2 Operators of quadratic forms of the creation and the annihilation operators; 9.4.3 Polynomials in R; of degree 2 10. Four notable roads to quantum dynamics |
| Record Nr. | UNINA-9910810359903321 |
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Hida Takeyuki <1927->
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| Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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