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Reconstruction of the modified discrete Langevin equation from persistent time series
1Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warsaw, Poland.
Abstract:
The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed.
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