Path Integrals for Stochastic Processes an Introduction
This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories, anticipating by two decades Feynman's f...
| Autor principal: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific Pub. Co
2013.
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| Colección: | EBSCO Academic eBook Collection Complete.
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| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b30863466*spi |
Tabla de Contenidos:
- Preface; 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.
- 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.
- 11.2.2 Example: Lotka-Volterra Model11.3 Kramers Problem; 12. Other Diffusion-Like Problems; 12.1 Diffusion in Shear Flows; 12.2 Diffusion Controlled Reactions; 12.2.1 The Model; 12.2.2 Point of View of Path Integrals; 12.2.3 Results for the Reaction A + B ₂!B; 13. What was Left Out; Appendix A Space-Time Transformation: Definitions and Solutions; A.1 Definitions; A.2 Solutions; Appendix B Basics Definitions in Fractional Calculus; Bibliography; Index.
