Lectures on white noise functionals:
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2008
|
Schlagworte: | |
Online-Zugang: | FAW01 FAW02 Volltext |
Beschreibung: | Includes bibliographical references (p. 253-261) and index 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 -- 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 Lévy's construction of Brownian motion. 2.5. Spaces [symbol], F and [symbol] arising from white noise. 2.6. Generalized white noise functionals. 2.7. Creation and annihilation operators. 2.8. Examples. 2.9. Addenda 3. Elemental random variables and Gaussian processes. 3.1. Elemental noises. 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 motion. 3.6. Fractional order differential operator in connection with Lévy'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. Lévy field and generalized Lévy 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 Lévy 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 [symbol]. 6.4. Applications -- 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 -- 10. Four notable roads to quantum dynamics. 10.1. White noise approach to path integrals. 10.2. Hamiltonian dynamics and Chern-Simons functional integrals. 10.3. Dirichlet forms. 10.4. Time operator. 10.5. Addendum: Euclidean fields White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications |
Beschreibung: | 1 Online-Ressource |
ISBN: | 9789812812049 9812812040 |
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100 | 1 | |a Hida, Takeyuki |e Verfasser |4 aut | |
245 | 1 | 0 | |a Lectures on white noise functionals |c by T. Hida & Si Si |
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500 | |a Includes bibliographical references (p. 253-261) and index | ||
500 | |a 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 -- 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 Lévy's construction of Brownian motion. 2.5. Spaces [symbol], F and [symbol] arising from white noise. 2.6. Generalized white noise functionals. 2.7. Creation and annihilation operators. 2.8. Examples. 2.9. Addenda | ||
500 | |a 3. Elemental random variables and Gaussian processes. 3.1. Elemental noises. 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 motion. 3.6. Fractional order differential operator in connection with Lévy'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. Lévy field and generalized Lévy field. 4.6. Gaussian elemental noises | ||
500 | |a 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 Lévy 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 [symbol]. 6.4. Applications -- 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 | ||
500 | |a 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 -- 10. Four notable roads to quantum dynamics. 10.1. White noise approach to path integrals. 10.2. Hamiltonian dynamics and Chern-Simons functional integrals. 10.3. Dirichlet forms. 10.4. Time operator. 10.5. Addendum: Euclidean fields | ||
500 | |a White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications | ||
650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
650 | 4 | |a White noise theory | |
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Datensatz im Suchindex
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---|---|
any_adam_object | |
author | Hida, Takeyuki |
author_facet | Hida, Takeyuki |
author_role | aut |
author_sort | Hida, Takeyuki |
author_variant | t h th |
building | Verbundindex |
bvnumber | BV043081709 |
collection | ZDB-4-EBA |
ctrlnum | (OCoLC)820944509 (DE-599)BVBBV043081709 |
dewey-full | 519.2/2 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.2/2 |
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dewey-sort | 3519.2 12 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Electronic eBook |
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language | English |
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spelling | Hida, Takeyuki Verfasser aut Lectures on white noise functionals by T. Hida & Si Si Singapore World Scientific Pub. Co. c2008 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 253-261) and index 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 -- 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 Lévy's construction of Brownian motion. 2.5. Spaces [symbol], F and [symbol] arising from white noise. 2.6. Generalized white noise functionals. 2.7. Creation and annihilation operators. 2.8. Examples. 2.9. Addenda 3. Elemental random variables and Gaussian processes. 3.1. Elemental noises. 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 motion. 3.6. Fractional order differential operator in connection with Lévy'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. Lévy field and generalized Lévy 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 Lévy 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 [symbol]. 6.4. Applications -- 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 -- 10. Four notable roads to quantum dynamics. 10.1. White noise approach to path integrals. 10.2. Hamiltonian dynamics and Chern-Simons functional integrals. 10.3. Dirichlet forms. 10.4. Time operator. 10.5. Addendum: Euclidean fields White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications MATHEMATICS / Probability & Statistics / General bisacsh White noise theory Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Weißes Rauschen (DE-588)4189502-2 gnd rswk-swf Weißes Rauschen (DE-588)4189502-2 s Gauß-Prozess (DE-588)4156111-9 s 1\p DE-604 Si, Si Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514719 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Hida, Takeyuki Lectures on white noise functionals MATHEMATICS / Probability & Statistics / General bisacsh White noise theory Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd Weißes Rauschen (DE-588)4189502-2 gnd |
subject_GND | (DE-588)4156111-9 (DE-588)4189502-2 |
title | Lectures on white noise functionals |
title_auth | Lectures on white noise functionals |
title_exact_search | Lectures on white noise functionals |
title_full | Lectures on white noise functionals by T. Hida & Si Si |
title_fullStr | Lectures on white noise functionals by T. Hida & Si Si |
title_full_unstemmed | Lectures on white noise functionals by T. Hida & Si Si |
title_short | Lectures on white noise functionals |
title_sort | lectures on white noise functionals |
topic | MATHEMATICS / Probability & Statistics / General bisacsh White noise theory Gaussian processes Gauß-Prozess (DE-588)4156111-9 gnd Weißes Rauschen (DE-588)4189502-2 gnd |
topic_facet | MATHEMATICS / Probability & Statistics / General White noise theory Gaussian processes Gauß-Prozess Weißes Rauschen |
url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514719 |
work_keys_str_mv | AT hidatakeyuki lecturesonwhitenoisefunctionals AT sisi lecturesonwhitenoisefunctionals |