White noise analysis and quantum information:
Saved in:
| Other Authors: | , , , , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New Jersey
World Scientific
[2018]
|
| Series: | Lecture notes series
vol. 34 |
| Subjects: | |
| Online Access: | FHN01 UEI01 Volltext |
| Item Description: | "According to the research program on Infinite Dimensional Analysis and Quantum Probability and their Applications (IDAQP), the workshop was held at the Institute for Mathematical Sciences (IMS) at the National University of Singapore (NUS) from 3rd of March to 7th of March, 2014" - Preface |
| Physical Description: | 1 Online-Ressource (xii, 230 Seiten) |
| ISBN: | 9789813225466 9789813225473 |
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| 245 | 1 | 0 | |a White noise analysis and quantum information |c editors Luigi Accardi, Louis H Y Chen, Takeyuki Hida, Masanori Ohya, Si Si, Noboru Watanabe |
| 264 | 1 | |a New Jersey |b World Scientific |c [2018] | |
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| 505 | 8 | |a Foreword; Preface; Extensions of Quantum Theory Canonically Associated to Classical Probability Measures; 1. Introduction; 2. The *-Algebra of Polynomial Functions; 2.1. The polynomial filtration; 2.2. The monomial gradation; 2.3. States on P and probability measures on R; 2.4. Connection with random variables; 2.5. The cyclic representation of (P, .,. ); 2.6. Real valued random variables as symmetric operators; 3. The -Orthogonal Polynomials; 3.1. The -orthogonal gradation of P; 3.2. The symmetric Jacobi relation; 3.3. Creation and annihilation operators | |
| 505 | 8 | |a 4. The 1-Dimensional Case4.1. Monic Jacobi relations; 4.2. Commutation relations in monic form; 4.3. The Gaussian case; 5. Probabilistic Extensions of Quantum Mechanics; 5.1. The generalized free evolution; 5.2. Equilibrium states; References; Hida Distribution Construction of Indefinite Metric ( p)d(d 4) Quantum Field Theory; 1. Short Review of a Probabilistic Formulation of Euclidean ( 4)2; 2. Formulation for d = 4; 3. Well Defined Terms (Feynman Graphs) for d = 4 as Hida Distributions; References; A Mathematical Realization of von Neumann's Measurement Scheme; 1. Introduction | |
| 505 | 8 | |a 2. Representation of Measurement Process2.1. Interaction between System and Apparatus; 2.2. Lifting Map and Decoherence Process; 2.3. Consistency with von Neumann's Scheme; References; On Random White Noise Processes with Memory for Time Series Analysis; 1. Introduction; 2. Random Variables with Memory; 3. Mean Square Displacement with Memory; 3.1. Wiener process; 3.2. Fractional Brownian motion; 3.3. Exponentially-modified Brownian motion; 4. Comparison with Empirical Data; 4.1. Vortex track fluctuations; 4.2. Particle-tracking in microrheology; 5. Conclusion; Acknowledgments; References | |
| 505 | 8 | |a Self-Repelling (Fractional) Brownian Motion Results and Open Questions1. Introduction; 2. The Edwards Model; 3. Dirichlet Forms; 4. Generalization to Fractional Brownian Motion; 5. Scaling of Self-Repelling Brownian Motion; 6. Open Questions; 6.1. The Flory index; 6.2. The Fisher-Redner-des Cloizeaux ""Theorem""; 6.3. Summary; Acknowledgments; References; Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus; 1. Introduction; 2. Stein's Method; 2.1. From characterization to approximation; 2.2. Stein identities and error terms; 2.3. Integration by parts | |
| 505 | 8 | |a 3. Hida Distributions3.1. White noise space; 3.2. The S-transform; 3.3. Test and generalized white noise functionals; 4. Hida Derivatives; 5. Integration by Parts Formula; 6. Connecting Stein's Method with Hida Calculus for White Noise Functionals; Acknowledgement; References; Sensitive Homology Searching Based on MTRAP Alignment; 1. Introduction; 2. MTRAP; 3. Homology Searching Based on MTRAP; 4. Performance Evaluation; 5. Conclusions; References; Some of the Future Directions of White Noise Theory; 1. Introduction; 2. Reductionism and Noise; 3. Spaces of Generalized White Noise Functionals | |
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Record in the Search Index
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| author2 | Accardi, Luigi 1947- Chen, Louis H. Y. 1940- Hida, Takeyuki 1927-2017 Ohya, Masanori 1947- Si, Si Watanabe, Noboru |
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| author_facet | Accardi, Luigi 1947- Chen, Louis H. Y. 1940- Hida, Takeyuki 1927-2017 Ohya, Masanori 1947- Si, Si Watanabe, Noboru |
| building | Verbundindex |
| bvnumber | BV044533565 |
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| contents | Foreword; Preface; Extensions of Quantum Theory Canonically Associated to Classical Probability Measures; 1. Introduction; 2. The *-Algebra of Polynomial Functions; 2.1. The polynomial filtration; 2.2. The monomial gradation; 2.3. States on P and probability measures on R; 2.4. Connection with random variables; 2.5. The cyclic representation of (P, .,. ); 2.6. Real valued random variables as symmetric operators; 3. The -Orthogonal Polynomials; 3.1. The -orthogonal gradation of P; 3.2. The symmetric Jacobi relation; 3.3. Creation and annihilation operators 4. The 1-Dimensional Case4.1. Monic Jacobi relations; 4.2. Commutation relations in monic form; 4.3. The Gaussian case; 5. Probabilistic Extensions of Quantum Mechanics; 5.1. The generalized free evolution; 5.2. Equilibrium states; References; Hida Distribution Construction of Indefinite Metric ( p)d(d 4) Quantum Field Theory; 1. Short Review of a Probabilistic Formulation of Euclidean ( 4)2; 2. Formulation for d = 4; 3. Well Defined Terms (Feynman Graphs) for d = 4 as Hida Distributions; References; A Mathematical Realization of von Neumann's Measurement Scheme; 1. Introduction 2. Representation of Measurement Process2.1. Interaction between System and Apparatus; 2.2. Lifting Map and Decoherence Process; 2.3. Consistency with von Neumann's Scheme; References; On Random White Noise Processes with Memory for Time Series Analysis; 1. Introduction; 2. Random Variables with Memory; 3. Mean Square Displacement with Memory; 3.1. Wiener process; 3.2. Fractional Brownian motion; 3.3. Exponentially-modified Brownian motion; 4. Comparison with Empirical Data; 4.1. Vortex track fluctuations; 4.2. Particle-tracking in microrheology; 5. Conclusion; Acknowledgments; References Self-Repelling (Fractional) Brownian Motion Results and Open Questions1. Introduction; 2. The Edwards Model; 3. Dirichlet Forms; 4. Generalization to Fractional Brownian Motion; 5. Scaling of Self-Repelling Brownian Motion; 6. Open Questions; 6.1. The Flory index; 6.2. The Fisher-Redner-des Cloizeaux ""Theorem""; 6.3. Summary; Acknowledgments; References; Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus; 1. Introduction; 2. Stein's Method; 2.1. From characterization to approximation; 2.2. Stein identities and error terms; 2.3. Integration by parts 3. Hida Distributions3.1. White noise space; 3.2. The S-transform; 3.3. Test and generalized white noise functionals; 4. Hida Derivatives; 5. Integration by Parts Formula; 6. Connecting Stein's Method with Hida Calculus for White Noise Functionals; Acknowledgement; References; Sensitive Homology Searching Based on MTRAP Alignment; 1. Introduction; 2. MTRAP; 3. Homology Searching Based on MTRAP; 4. Performance Evaluation; 5. Conclusions; References; Some of the Future Directions of White Noise Theory; 1. Introduction; 2. Reductionism and Noise; 3. Spaces of Generalized White Noise Functionals |
| ctrlnum | (OCoLC)1011418794 (DE-599)BVBBV044533565 |
| discipline | Mathematik |
| format | Electronic eBook |
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| series | Lecture notes series |
| series2 | Lecture notes series |
| spelling | White noise analysis and quantum information editors Luigi Accardi, Louis H Y Chen, Takeyuki Hida, Masanori Ohya, Si Si, Noboru Watanabe New Jersey World Scientific [2018] 1 Online-Ressource (xii, 230 Seiten) txt rdacontent c rdamedia cr rdacarrier Lecture notes series vol. 34 "According to the research program on Infinite Dimensional Analysis and Quantum Probability and their Applications (IDAQP), the workshop was held at the Institute for Mathematical Sciences (IMS) at the National University of Singapore (NUS) from 3rd of March to 7th of March, 2014" - Preface Foreword; Preface; Extensions of Quantum Theory Canonically Associated to Classical Probability Measures; 1. Introduction; 2. The *-Algebra of Polynomial Functions; 2.1. The polynomial filtration; 2.2. The monomial gradation; 2.3. States on P and probability measures on R; 2.4. Connection with random variables; 2.5. The cyclic representation of (P, .,. ); 2.6. Real valued random variables as symmetric operators; 3. The -Orthogonal Polynomials; 3.1. The -orthogonal gradation of P; 3.2. The symmetric Jacobi relation; 3.3. Creation and annihilation operators 4. The 1-Dimensional Case4.1. Monic Jacobi relations; 4.2. Commutation relations in monic form; 4.3. The Gaussian case; 5. Probabilistic Extensions of Quantum Mechanics; 5.1. The generalized free evolution; 5.2. Equilibrium states; References; Hida Distribution Construction of Indefinite Metric ( p)d(d 4) Quantum Field Theory; 1. Short Review of a Probabilistic Formulation of Euclidean ( 4)2; 2. Formulation for d = 4; 3. Well Defined Terms (Feynman Graphs) for d = 4 as Hida Distributions; References; A Mathematical Realization of von Neumann's Measurement Scheme; 1. Introduction 2. Representation of Measurement Process2.1. Interaction between System and Apparatus; 2.2. Lifting Map and Decoherence Process; 2.3. Consistency with von Neumann's Scheme; References; On Random White Noise Processes with Memory for Time Series Analysis; 1. Introduction; 2. Random Variables with Memory; 3. Mean Square Displacement with Memory; 3.1. Wiener process; 3.2. Fractional Brownian motion; 3.3. Exponentially-modified Brownian motion; 4. Comparison with Empirical Data; 4.1. Vortex track fluctuations; 4.2. Particle-tracking in microrheology; 5. Conclusion; Acknowledgments; References Self-Repelling (Fractional) Brownian Motion Results and Open Questions1. Introduction; 2. The Edwards Model; 3. Dirichlet Forms; 4. Generalization to Fractional Brownian Motion; 5. Scaling of Self-Repelling Brownian Motion; 6. Open Questions; 6.1. The Flory index; 6.2. The Fisher-Redner-des Cloizeaux ""Theorem""; 6.3. Summary; Acknowledgments; References; Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus; 1. Introduction; 2. Stein's Method; 2.1. From characterization to approximation; 2.2. Stein identities and error terms; 2.3. Integration by parts 3. Hida Distributions3.1. White noise space; 3.2. The S-transform; 3.3. Test and generalized white noise functionals; 4. Hida Derivatives; 5. Integration by Parts Formula; 6. Connecting Stein's Method with Hida Calculus for White Noise Functionals; Acknowledgement; References; Sensitive Homology Searching Based on MTRAP Alignment; 1. Introduction; 2. MTRAP; 3. Homology Searching Based on MTRAP; 4. Performance Evaluation; 5. Conclusions; References; Some of the Future Directions of White Noise Theory; 1. Introduction; 2. Reductionism and Noise; 3. Spaces of Generalized White Noise Functionals Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Weißes Rauschen (DE-588)4189502-2 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 gnd rswk-swf White noise theory Stochastic processes Spectral energy distribution MATHEMATICS / Applied MATHEMATICS / Probability & Statistics / General Electronic books (DE-588)1071861417 Konferenzschrift 2014 Singapur gnd-content Weißes Rauschen (DE-588)4189502-2 s Stochastischer Prozess (DE-588)4057630-9 s Quanteninformatik (DE-588)4705961-8 s 1\p DE-604 Accardi, Luigi 1947- (DE-588)172488729 edt Chen, Louis H. Y. 1940- (DE-588)112808506 edt Hida, Takeyuki 1927-2017 (DE-588)124605257 edt Ohya, Masanori 1947- (DE-588)133939693 edt Si, Si edt Watanabe, Noboru edt Erscheint auch als Druck-Ausgabe 978-981-3225-45-9 Lecture notes series vol. 34 (DE-604)BV017225650 34 http://www.worldscientific.com/worldscibooks/10.1142/10582#t=toc Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | White noise analysis and quantum information Lecture notes series Foreword; Preface; Extensions of Quantum Theory Canonically Associated to Classical Probability Measures; 1. Introduction; 2. The *-Algebra of Polynomial Functions; 2.1. The polynomial filtration; 2.2. The monomial gradation; 2.3. States on P and probability measures on R; 2.4. Connection with random variables; 2.5. The cyclic representation of (P, .,. ); 2.6. Real valued random variables as symmetric operators; 3. The -Orthogonal Polynomials; 3.1. The -orthogonal gradation of P; 3.2. The symmetric Jacobi relation; 3.3. Creation and annihilation operators 4. The 1-Dimensional Case4.1. Monic Jacobi relations; 4.2. Commutation relations in monic form; 4.3. The Gaussian case; 5. Probabilistic Extensions of Quantum Mechanics; 5.1. The generalized free evolution; 5.2. Equilibrium states; References; Hida Distribution Construction of Indefinite Metric ( p)d(d 4) Quantum Field Theory; 1. Short Review of a Probabilistic Formulation of Euclidean ( 4)2; 2. Formulation for d = 4; 3. Well Defined Terms (Feynman Graphs) for d = 4 as Hida Distributions; References; A Mathematical Realization of von Neumann's Measurement Scheme; 1. Introduction 2. Representation of Measurement Process2.1. Interaction between System and Apparatus; 2.2. Lifting Map and Decoherence Process; 2.3. Consistency with von Neumann's Scheme; References; On Random White Noise Processes with Memory for Time Series Analysis; 1. Introduction; 2. Random Variables with Memory; 3. Mean Square Displacement with Memory; 3.1. Wiener process; 3.2. Fractional Brownian motion; 3.3. Exponentially-modified Brownian motion; 4. Comparison with Empirical Data; 4.1. Vortex track fluctuations; 4.2. Particle-tracking in microrheology; 5. Conclusion; Acknowledgments; References Self-Repelling (Fractional) Brownian Motion Results and Open Questions1. Introduction; 2. The Edwards Model; 3. Dirichlet Forms; 4. Generalization to Fractional Brownian Motion; 5. Scaling of Self-Repelling Brownian Motion; 6. Open Questions; 6.1. The Flory index; 6.2. The Fisher-Redner-des Cloizeaux ""Theorem""; 6.3. Summary; Acknowledgments; References; Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus; 1. Introduction; 2. Stein's Method; 2.1. From characterization to approximation; 2.2. Stein identities and error terms; 2.3. Integration by parts 3. Hida Distributions3.1. White noise space; 3.2. The S-transform; 3.3. Test and generalized white noise functionals; 4. Hida Derivatives; 5. Integration by Parts Formula; 6. Connecting Stein's Method with Hida Calculus for White Noise Functionals; Acknowledgement; References; Sensitive Homology Searching Based on MTRAP Alignment; 1. Introduction; 2. MTRAP; 3. Homology Searching Based on MTRAP; 4. Performance Evaluation; 5. Conclusions; References; Some of the Future Directions of White Noise Theory; 1. Introduction; 2. Reductionism and Noise; 3. Spaces of Generalized White Noise Functionals Stochastischer Prozess (DE-588)4057630-9 gnd Weißes Rauschen (DE-588)4189502-2 gnd Quanteninformatik (DE-588)4705961-8 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4189502-2 (DE-588)4705961-8 (DE-588)1071861417 |
| title | White noise analysis and quantum information |
| title_auth | White noise analysis and quantum information |
| title_exact_search | White noise analysis and quantum information |
| title_full | White noise analysis and quantum information editors Luigi Accardi, Louis H Y Chen, Takeyuki Hida, Masanori Ohya, Si Si, Noboru Watanabe |
| title_fullStr | White noise analysis and quantum information editors Luigi Accardi, Louis H Y Chen, Takeyuki Hida, Masanori Ohya, Si Si, Noboru Watanabe |
| title_full_unstemmed | White noise analysis and quantum information editors Luigi Accardi, Louis H Y Chen, Takeyuki Hida, Masanori Ohya, Si Si, Noboru Watanabe |
| title_short | White noise analysis and quantum information |
| title_sort | white noise analysis and quantum information |
| topic | Stochastischer Prozess (DE-588)4057630-9 gnd Weißes Rauschen (DE-588)4189502-2 gnd Quanteninformatik (DE-588)4705961-8 gnd |
| topic_facet | Stochastischer Prozess Weißes Rauschen Quanteninformatik Konferenzschrift 2014 Singapur |
| url | http://www.worldscientific.com/worldscibooks/10.1142/10582#t=toc |
| volume_link | (DE-604)BV017225650 |
| work_keys_str_mv | AT accardiluigi whitenoiseanalysisandquantuminformation AT chenlouishy whitenoiseanalysisandquantuminformation AT hidatakeyuki whitenoiseanalysisandquantuminformation AT ohyamasanori whitenoiseanalysisandquantuminformation AT sisi whitenoiseanalysisandquantuminformation AT watanabenoboru whitenoiseanalysisandquantuminformation |