LEADER 04438oam 2200493 450 001 9910792054403321 005 20190911112728.0 010 $a1-299-28135-4 010 $a981-4449-04-0 035 $a(OCoLC)897557790 035 $a(MiFhGG)GVRL8RGQ 035 $a(EXLCZ)992560000000099543 100 $a20130716h20132013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aPath integrals for stochastic processes $ean introduction /$fHoracio S. Wio, Instituto de Fisica de Cantabria, Universidad de Cantabria, and CSIC, Spain 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$dc2013 210 1$aNew Jersey :$cWorld Scientific,$d[2013] 210 4$d?2013 215 $a1 online resource (xiii, 159 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a981-4447-99-4 320 $aIncludes bibliographical references (p. 149-155) and index. 327 $aPreface; 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 327 $a4. 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 327 $a6.6 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 ?; 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 327 $a10. 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 330 $aThis 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 606 $aStochastic processes 606 $aPath integrals 615 0$aStochastic processes. 615 0$aPath integrals. 676 $a530.1595 700 $aWio$b Horacio S$0753173 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910792054403321 996 $aPath integrals for stochastic processes$93817956 997 $aUNINA