Abstract
Using the theory of Markovian diffusion processes it is established that a non-linear Fokker-Planck equation is the most general continuous asymptotic representation of master equations describing internal fluctuations in the limit of large systems. The good agreement between the results of the Fokker-Planck approximation and those of the master equation description is demonstrated on several examples. The differences with van Kampen's approach are elucidated.
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Horsthemke, W., Brenig, L. Non-linear Fokker-Planck equation as an asymptotic representation of the master equation. Z Physik B 27, 341–348 (1977). https://doi.org/10.1007/BF01320526
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DOI: https://doi.org/10.1007/BF01320526