Abstract
A new proof of the diffusion approximation for ordinary differential equations is given. It is based on an asymptotic expansion of the solution of the corresponding Liouville partial differential equations. In contrast to previous results obtained for the suspension under Holderian mappings of subshift of finite type or Fourier analysis techniques, our proof relies only on symbolic dynamics.
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Dogbé, C. Asymptotic Behavior for the Liouville Equations. Journal of Statistical Physics 99, 873–902 (2000). https://doi.org/10.1023/A:1018647613468
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DOI: https://doi.org/10.1023/A:1018647613468