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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 / / 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 |
|
Hida Takeyuki <1927->
|
||
| Hackensack, NJ, : World Scientific, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Selected papers of Takeyuki Hida [[electronic resource] /] / edited by L. Accardi ... [et al.]
| Selected papers of Takeyuki Hida [[electronic resource] /] / edited by L. Accardi ... [et al.] |
| Autore | Hida Takeyuki <1927-> |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (496 p.) |
| Disciplina | 519.5 |
| Altri autori (Persone) | AccardiL <1947-> (Luigi) |
| Soggetto topico |
Stochastic processes
Probabilities |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-93455-0
9786611934552 981-279-461-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910454373803321 |
|
Hida Takeyuki <1927->
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Selected papers of Takeyuki Hida / / edited by L. Accardi ... [et al.]
| Selected papers of Takeyuki Hida / / edited by L. Accardi ... [et al.] |
| Autore | Hida Takeyuki <1927-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; River Edge, N.J., : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (496 p.) |
| Disciplina | 519.5 |
| Altri autori (Persone) | AccardiL <1947-> (Luigi) |
| Soggetto topico |
Stochastic processes
Probabilities |
| ISBN |
1-281-93455-0
9786611934552 981-279-461-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910825820103321 |
|
Hida Takeyuki <1927->
|
||
| Singapore ; ; River Edge, N.J., : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||