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Reduction of the Number of Variables

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

Abstract

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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References

  1. R. L. Stratonovich: Topics in the Theory of Random Noise, Vol. I (Gordon and Breach, New York 1963) p. 79ff.

    Google Scholar 

  2. G. H. Weiss: Ad. Chem. Phys. 13, 1 (1966)

    Article  Google Scholar 

  3. M. A. Burschka, U. M. Titulaer: J. Stat. Phys. 25, 569 and 26, 59 (1981)

    Google Scholar 

  4. M. A. Burschka, U. M. Titulaer: Physica 112A, 315 (1982)

    ADS  Google Scholar 

  5. A. Schenzle, H. Brand: Phys. Rev. A20, 1628 (1979)

    ADS  Google Scholar 

  6. H. Brand, A. Schenzle: Phys. Lett. 81A, 321 (1981)

    MathSciNet  ADS  Google Scholar 

  7. K. Kaneko: Progr. Theor. Phys. 66, 129 (1981)

    Article  ADS  Google Scholar 

  8. O. Madelung: Introduction to Solid-State Theory, Springer Ser. Solid-State Sci., Vol. 2 (Springer, Berlin, Heidelberg, New York 1978) p. 9

    Google Scholar 

  9. R. W. Zwanzig: Lectures in Theoretical Physics, Vol. 3 (Wiley-Interscience, New York 1961)

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© 1996 Springer-Verlag Berlin Heidelberg

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Risken, H. (1996). Reduction of the Number of Variables. In: The Fokker-Planck Equation. Springer Series in Synergetics, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61544-3_8

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  • DOI: https://doi.org/10.1007/978-3-642-61544-3_8

  • 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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