Path Integrals for Stochastic Processes : an Introduction.

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Wio, Horacio S.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore : World Scientific Pub. Co., 2013.
Temas:
Stochastic integrals.
Function spaces.
Intégrales stochastiques.
Espaces fonctionnels.
SCIENCE > Physics > Mathematical & Computational.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 I. 4.1. 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
  • 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 solutions. 6.7. 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
  • 8. Non-Markov processes: Non-Gaussian case. 8.1. Introduction. 8.2. Non-Gaussian process [symbol]. 8.3. Effective Markov approximation
  • 9. Non-Markov processes: nonlinear cases. 9.1. Introduction. 9.2. Nonlinear noise. 9.3. Kramers problem
  • 10. Fractional diffusion process. 10.1. 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. 10.5. Fractional Lévy motion: path integral approach. 10.6. Fractional Lévy motion: final comments
  • 11. Feynman-Kac Formula, the influence functional. 11.1. Feynman-Kac formula. 11.2. Influence functional: elimination of irrelevant variables. 11.3. Kramers problem
  • 12. Other diffusion-like problems. 12.1. Diffusion in shear flows. 12.2. Diffusion controlled reactions
  • 13. What was left out.

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