04438oam 2200493 450 991081065370332120190911112728.01-299-28135-4981-4449-04-0(OCoLC)897557790(MiFhGG)GVRL8RGQ(EXLCZ)99256000000009954320130716h20132013 uy 0engurun|---uuuuatxtccrPath integrals for stochastic processes an introduction /Horacio S. Wio, Instituto de Fisica de Cantabria, Universidad de Cantabria, and CSIC, SpainSingapore ;Hackensack, N.J. World Scientificc2013New Jersey :World Scientific,[2013]�20131 online resource (xiii, 159 pages) illustrationsGale eBooksDescription based upon print version of record.981-4447-99-4 Includes bibliographical references (p. 149-155) and index.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 Path4. 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 Conditions6.6 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 Problem10. 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 NoiseThis 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 famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950's. The last quarter of the 20th century has witnesseStochastic processesPath integralsStochastic processes.Path integrals.530.1595Wio Horacio S753173MiFhGGMiFhGGBOOK9910810653703321Path integrals for stochastic processes4061030UNINA