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Path integrals for stochastic processes [[electronic resource] ] : an introduction / / Horacio S. Wio
| Path integrals for stochastic processes [[electronic resource] ] : an introduction / / Horacio S. Wio |
| Autore | Wio Horacio S |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2013 |
| Descrizione fisica | 1 online resource (174 p.) |
| Disciplina | 530.1595 |
| Soggetto topico |
Function spaces
Stochastic integrals |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-299-28135-4
981-4449-04-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Stochastic Processes: A Short Tour; 1.1 Stochastic Process; 1.2 Master Equation; 1.3 Langevin Equation; 1.4 Fokker-Planck Equation; 1.5 Relation Between Langevin and Fokker-Planck Equations; 2. The Path Integral for a Markov Stochastic Process; 2.1 The Wiener Integral; 2.2 The Path Integral for a General Markov Process; 2.3 The Recovering of the Fokker-Planck Equation; 2.4 Path Integrals in Phase Space; 2.5 Generating Functional and Correlations; 3. Generalized Path Expansion Scheme I; 3.1 Expansion Around the Reference Path; 3.2 Fluctuations Around the Reference Path
4. Space-Time Transformation I4.1 Introduction; 4.2 Simple Example; 4.3 Fluctuation Theorems from Non-equilibrium Onsager- Machlup Theory; 4.4 Brownian Particle in a Time-Dependent Harmonic Potential; 4.5 Work Distribution Function; 5. Generalized Path Expansion Scheme II; 5.1 Path Expansion: Further Aspects; 5.2 Examples; 5.2.1 Ornstein-Uhlenbeck Problem; 5.2.2 Simplified Prey-Predator Model; 6. Space-Time Transformation II; 6.1 Introduction; 6.2 The Diffusion Propagator; 6.3 Flow Through the Infinite Barrier; 6.4 Asymptotic Probability Distribution; 6.5 General Localization Conditions 6.6 A Family of Analytical Solutions6.7 Stochastic Resonance in a Monostable Non-Harmonic Time-Dependent Potential; 7. Non-Markov Processes: Colored Noise Case; 7.1 Introduction; 7.2 Ornstein-Uhlenbeck Case; 7.3 The Stationary Distribution; 7.4 The Interpolating Scheme; 7.4.1 Stationary Distributions; 8. Non-Markov Processes: Non-Gaussian Case; 8.1 Introduction; 8.2 Non-Gaussian Process η; 8.3 Effective Markov Approximation; 9. Non-Markov Processes: Nonlinear Cases; 9.1 Introduction; 9.2 Nonlinear Noise; 9.2.1 Polynomial Noise; 9.2.2 Exponential Noise; 9.3 Kramers Problem 10. Fractional Diffusion Process10.1 Short Introduction to Fractional Brownian Motion; 10.2 Fractional Brownian Motion: A Path Integral Approach; 10.3 Fractional Brownian Motion: The Kinetic Equation; 10.4 Fractional Brownian Motion: Some Extensions; 10.4.1 Case 1; 10.4.2 Case 2; 10.5 Fractional Levy Motion: Path Integral Approach; 10.5.1 Gaussian Test; 10.5.2 Kinetic Equation; 10.6 Fractional Levy Motion: Final Comments; 11. Feynman-Kac Formula, the Influence Functional; 11.1 Feynman-Kac formula; 11.2 Influence Functional: Elimination of Irrelevant Variables; 11.2.1 Example: Colored Noise |
| Record Nr. | UNINA-9910465837103321 |
Wio Horacio S
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Path integrals for stochastic processes : an introduction / / Horacio S. Wio, Instituto de Fisica de Cantabria, Universidad de Cantabria, and CSIC, Spain
| Path integrals for stochastic processes : an introduction / / Horacio S. Wio, Instituto de Fisica de Cantabria, Universidad de Cantabria, and CSIC, Spain |
| Autore | Wio Horacio S |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2013 |
| Descrizione fisica | 1 online resource (xiii, 159 pages) : illustrations |
| Disciplina | 530.1595 |
| Collana | Gale eBooks |
| Soggetto topico |
Stochastic processes
Path integrals |
| ISBN |
1-299-28135-4
981-4449-04-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Stochastic Processes: A Short Tour; 1.1 Stochastic Process; 1.2 Master Equation; 1.3 Langevin Equation; 1.4 Fokker-Planck Equation; 1.5 Relation Between Langevin and Fokker-Planck Equations; 2. The Path Integral for a Markov Stochastic Process; 2.1 The Wiener Integral; 2.2 The Path Integral for a General Markov Process; 2.3 The Recovering of the Fokker-Planck Equation; 2.4 Path Integrals in Phase Space; 2.5 Generating Functional and Correlations; 3. Generalized Path Expansion Scheme I; 3.1 Expansion Around the Reference Path; 3.2 Fluctuations Around the Reference Path
4. Space-Time Transformation I4.1 Introduction; 4.2 Simple Example; 4.3 Fluctuation Theorems from Non-equilibrium Onsager- Machlup Theory; 4.4 Brownian Particle in a Time-Dependent Harmonic Potential; 4.5 Work Distribution Function; 5. Generalized Path Expansion Scheme II; 5.1 Path Expansion: Further Aspects; 5.2 Examples; 5.2.1 Ornstein-Uhlenbeck Problem; 5.2.2 Simplified Prey-Predator Model; 6. Space-Time Transformation II; 6.1 Introduction; 6.2 The Diffusion Propagator; 6.3 Flow Through the Infinite Barrier; 6.4 Asymptotic Probability Distribution; 6.5 General Localization Conditions 6.6 A Family of Analytical Solutions6.7 Stochastic Resonance in a Monostable Non-Harmonic Time-Dependent Potential; 7. Non-Markov Processes: Colored Noise Case; 7.1 Introduction; 7.2 Ornstein-Uhlenbeck Case; 7.3 The Stationary Distribution; 7.4 The Interpolating Scheme; 7.4.1 Stationary Distributions; 8. Non-Markov Processes: Non-Gaussian Case; 8.1 Introduction; 8.2 Non-Gaussian Process η; 8.3 Effective Markov Approximation; 9. Non-Markov Processes: Nonlinear Cases; 9.1 Introduction; 9.2 Nonlinear Noise; 9.2.1 Polynomial Noise; 9.2.2 Exponential Noise; 9.3 Kramers Problem 10. Fractional Diffusion Process10.1 Short Introduction to Fractional Brownian Motion; 10.2 Fractional Brownian Motion: A Path Integral Approach; 10.3 Fractional Brownian Motion: The Kinetic Equation; 10.4 Fractional Brownian Motion: Some Extensions; 10.4.1 Case 1; 10.4.2 Case 2; 10.5 Fractional Levy Motion: Path Integral Approach; 10.5.1 Gaussian Test; 10.5.2 Kinetic Equation; 10.6 Fractional Levy Motion: Final Comments; 11. Feynman-Kac Formula, the Influence Functional; 11.1 Feynman-Kac formula; 11.2 Influence Functional: Elimination of Irrelevant Variables; 11.2.1 Example: Colored Noise |
| Record Nr. | UNINA-9910792054403321 |
|
Wio Horacio S
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Path integrals for stochastic processes : an introduction / / Horacio S. Wio, Instituto de Fisica de Cantabria, Universidad de Cantabria, and CSIC, Spain
| Path integrals for stochastic processes : an introduction / / Horacio S. Wio, Instituto de Fisica de Cantabria, Universidad de Cantabria, and CSIC, Spain |
| Autore | Wio Horacio S |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, c2013 |
| Descrizione fisica | 1 online resource (xiii, 159 pages) : illustrations |
| Disciplina | 530.1595 |
| Collana | Gale eBooks |
| Soggetto topico |
Stochastic processes
Path integrals |
| ISBN |
1-299-28135-4
981-4449-04-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Stochastic Processes: A Short Tour; 1.1 Stochastic Process; 1.2 Master Equation; 1.3 Langevin Equation; 1.4 Fokker-Planck Equation; 1.5 Relation Between Langevin and Fokker-Planck Equations; 2. The Path Integral for a Markov Stochastic Process; 2.1 The Wiener Integral; 2.2 The Path Integral for a General Markov Process; 2.3 The Recovering of the Fokker-Planck Equation; 2.4 Path Integrals in Phase Space; 2.5 Generating Functional and Correlations; 3. Generalized Path Expansion Scheme I; 3.1 Expansion Around the Reference Path; 3.2 Fluctuations Around the Reference Path
4. Space-Time Transformation I4.1 Introduction; 4.2 Simple Example; 4.3 Fluctuation Theorems from Non-equilibrium Onsager- Machlup Theory; 4.4 Brownian Particle in a Time-Dependent Harmonic Potential; 4.5 Work Distribution Function; 5. Generalized Path Expansion Scheme II; 5.1 Path Expansion: Further Aspects; 5.2 Examples; 5.2.1 Ornstein-Uhlenbeck Problem; 5.2.2 Simplified Prey-Predator Model; 6. Space-Time Transformation II; 6.1 Introduction; 6.2 The Diffusion Propagator; 6.3 Flow Through the Infinite Barrier; 6.4 Asymptotic Probability Distribution; 6.5 General Localization Conditions 6.6 A Family of Analytical Solutions6.7 Stochastic Resonance in a Monostable Non-Harmonic Time-Dependent Potential; 7. Non-Markov Processes: Colored Noise Case; 7.1 Introduction; 7.2 Ornstein-Uhlenbeck Case; 7.3 The Stationary Distribution; 7.4 The Interpolating Scheme; 7.4.1 Stationary Distributions; 8. Non-Markov Processes: Non-Gaussian Case; 8.1 Introduction; 8.2 Non-Gaussian Process η; 8.3 Effective Markov Approximation; 9. Non-Markov Processes: Nonlinear Cases; 9.1 Introduction; 9.2 Nonlinear Noise; 9.2.1 Polynomial Noise; 9.2.2 Exponential Noise; 9.3 Kramers Problem 10. Fractional Diffusion Process10.1 Short Introduction to Fractional Brownian Motion; 10.2 Fractional Brownian Motion: A Path Integral Approach; 10.3 Fractional Brownian Motion: The Kinetic Equation; 10.4 Fractional Brownian Motion: Some Extensions; 10.4.1 Case 1; 10.4.2 Case 2; 10.5 Fractional Levy Motion: Path Integral Approach; 10.5.1 Gaussian Test; 10.5.2 Kinetic Equation; 10.6 Fractional Levy Motion: Final Comments; 11. Feynman-Kac Formula, the Influence Functional; 11.1 Feynman-Kac formula; 11.2 Influence Functional: Elimination of Irrelevant Variables; 11.2.1 Example: Colored Noise |
| Record Nr. | UNINA-9910810653703321 |
|
Wio Horacio S
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||