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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 | ||
| ||