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Record Nr. |
UNINA9910792054403321 |
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Autore |
Wio Horacio S |
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Titolo |
Path integrals for stochastic processes : an introduction / / Horacio S. Wio, Instituto de Fisica de Cantabria, Universidad de Cantabria, and CSIC, Spain |
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Pubbl/distr/stampa |
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Singapore ; ; Hackensack, N.J., : World Scientific, c2013 |
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New Jersey : , : World Scientific, , [2013] |
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�2013 |
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ISBN |
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1-299-28135-4 |
981-4449-04-0 |
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Descrizione fisica |
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1 online resource (xiii, 159 pages) : illustrations |
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Collana |
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Disciplina |
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Soggetti |
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Stochastic processes |
Path integrals |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 149-155) and index. |
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Nota di contenuto |
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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 |
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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 |
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Sommario/riassunto |
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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 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 witnesse |
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