Reduction of the Number of Variables

  • Hannes Risken
Part of the Springer Series in Synergetics book series (SSSYN, volume 18)


Usually, the difficulty of solving the Fokker-Planck equation like any other partial differential equation increases with increasing number of independent variables. It is therefore advisable to eliminate as many variables as possible, so we discuss below three cases where the number of independent variables can be reduced.


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  1. 8.1
    R. L. Stratonovich: Topics in the Theory of Random Noise, Vol. I (Gordon and Breach, New York 1963) p. 79 ff.Google Scholar
  2. 8.2
    G. H. Weiss: Adv. Chem. Phys. 13, 1 (1966)CrossRefGoogle Scholar
  3. 8.3
    M. A. Burschka, U. M. Titulaer: J. Stat. Phys. 25, 569 and 26, 59 (1981)ADSCrossRefGoogle Scholar
  4. 8.4
    M. A. Burschka, U. M. Titulaer: Physica 112A, 315 (1982)ADSGoogle Scholar
  5. 8.5
    A. Schenzle, H. Brand: Phys. Rev. A20, 1628 (1979)ADSGoogle Scholar
  6. 8.6
    H. Brand, A. Schenzle: Phys. Lett. 81A, 321 (1981)MathSciNetADSGoogle Scholar
  7. 8.7
    K. Kaneko: Progr. Theor. Phys. 66, 129 (1981)ADSCrossRefGoogle Scholar
  8. 8.8
    O. Madelung: Introduction to Solid-State Theory, Springer Ser. Solid-State Sci., Vol. 2 (Springer, Berlin, Heidelberg, New York 1978) p. 9Google Scholar
  9. 8.9
    R. W. Zwanzig: Lectures in Theoretical Physics, Vol. 3 (Wiley-Interscience, New York 1961)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Hannes Risken
    • 1
  1. 1.Abteilung für Theoretische PhysikUniversität UlmUlmFed. Rep. of Germany

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