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Introduction

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The Fokker-Planck Equation

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 18))

Abstract

A Fokker-Planck equation was first used by Fokker [1.1] and Planck [1.2] to describe the Brownian motion of particles. To become familiar with this equation we first discuss the Brownian motion of particles in its simplest form.

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References

  1. A. D. Fokker: Ann. Physik 43, 810 (1914)

    Article  ADS  Google Scholar 

  2. M. Planck: Sitzber. Preuß. Akad. Wiss. p. 324 (1917)

    Google Scholar 

  3. P. Langevin: Comptes rendus 146, 530 (1908)

    MATH  Google Scholar 

  4. A. Einstein: Ann. Physik 17, 549 (1905) and 19, 371 (1906)

    Article  ADS  Google Scholar 

  5. G. E. Uhlenbeck, L. S. Ornstein: Phys. Rev. 36, 823 (1930)

    Article  ADS  Google Scholar 

  6. S. Chandrasekhar: Rev. Mod. Phys.15, 1 (1943)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. M. C. Wang, G. E. Uhlenbeck: Rev. Mod. Phys. 17, 323 (1945)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. References [1.5-7] and other articles are contained in: N. Wax (ed.): Selected Papers on Noise and Stochastic Processes (Dover, New York 1954)

    MATH  Google Scholar 

  9. A. T. Bharucha-Reid: Elements of the Theory of Markov Processes and Their Applications (McGraw-Hill, New York 1960)

    MATH  Google Scholar 

  10. R. L. Stratonovich: Topics in the Theory of Random Noise, Vols. I and II (Gordon & Breach, New York 1963 and 1967)

    Google Scholar 

  11. M. Lax: Rev. Mod. Phys. 32, 25 (1960) (a), 38, 359 (1966) (b) and 38, 541 (1966) (c)

    Article  ADS  MATH  Google Scholar 

  12. N. S. Goel, N. Richter-Dyn: Stochastic Models in Biology (Academic, New York 1974)

    Google Scholar 

  13. H. Haken: Rev. Mod. Phys. 47, 67 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  14. H. Haken: Synergetics, An Introduction, 3rd ed. Springer Ser. Synergetics, Vol. 1 (Springer, Berlin, Heidelberg, New York 1983)

    MATH  Google Scholar 

  15. Z. Schuss: Theory and Applications of Stochastic Differential Equations (Wiley, New York 1980)

    MATH  Google Scholar 

  16. O. Klein: Arkiv for Mathematik, Astronomi, och Fysik 16, No 5 (1921)

    Google Scholar 

  17. H. A. Kramers: Physica 7, 284 (1940)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. M. v. Smoluchowski: Ann. Physik 48, 1103 (1915)

    ADS  Google Scholar 

  19. J. E. Moyal: J. Roy. Stat. Soc. (London) B 11, 150 (1949)

    MathSciNet  Google Scholar 

  20. L. Boltzmann: Lectures on Gas Theory, transl. by S. Brush (University of California Press, Berkley 1964)

    Google Scholar 

  21. R. Balescu: Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York 1975) Chap. 11

    MATH  Google Scholar 

  22. P. Résibois, M. De Leener: Classical Kinetic Theory of Fluids (Wiley, New York 1977) Chap. 9

    Google Scholar 

  23. P. L. Bhatnagar, E. P. Gross, M. Krook: Phys. Rev. 94, 511 (1954)

    Article  ADS  MATH  Google Scholar 

  24. N. G. van Kampen: Adv. Chem. Phys. 34, 245 (1976)

    Article  Google Scholar 

  25. I. Prigogine, P. Résibois: Physica 24, 795 (1958)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. S. Nakajima: Prog. Theor. Phys. 20, 948 (1958)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. R. W. Zwanzig: J. Chem. Phys. 33, 1338 (1960)

    Article  MathSciNet  ADS  Google Scholar 

  28. F. Haake: Springer Tracts Mod. Phys. 66, 98 (Springer, Berlin, Heidelberg, New York 1973)

    Google Scholar 

  29. V. M. Kenkre: In Statistical Mechanics and Statistical Methods in Theory and Applications, ed. by U. Landmann (Plenum, New York 1977) p. 441

    Google Scholar 

  30. H. Grabert: Springer Tracts Mod. Phys. 95 (Springer, Berlin, Heidelberg, New York 1982)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Abteilung für Theoretische Physik, Universität Ulm, D-89081, Oberer Eselsberg, Ulm, Germany

    Professor Dr. Hannes Risken

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  1. Professor Dr. Hannes Risken
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© 1996 Springer-Verlag Berlin Heidelberg

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Risken, H. (1996). Introduction. In: The Fokker-Planck Equation. Springer Series in Synergetics, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61544-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-61544-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61530-9

  • Online ISBN: 978-3-642-61544-3

  • eBook Packages: Springer Book Archive

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