Zeitschrift für Physik B Condensed Matter

, Volume 43, Issue 2, pp 185–187 | Cite as

Chapman-Kolmogorov equation and path integrals for discrete chaos in presence of noise

  • H. Haken
  • G. Mayer-Kress


We derive an equation of the Chapman-Kolmogorov type for discrete multi-dimensional mappings under the action of additive and multiplicative noise with arbitrary distribution function. The resulting equation is reduced to a Fredholm integral equation. By iteration of the Chapman-Kolmogorov equation as usual, a path integral solution is found. Specializing the distribution function of the noise to a Gaussian distribution and taking the Fourier transform contant can be made with the path integral formulation used by Shraiman, Wayne and Martin.


Neural Network Fourier Fourier Transform Distribution Function Gaussian Distribution 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • H. Haken
    • 1
  • G. Mayer-Kress
    • 1
  1. 1.Institut für Theoretische Physik der UniversitätStuttgartGermany

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