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arXiv · 1102.5264

Estimation of Kramers-Moyal coefficients at low sampling rates

Christoph Honisch·Rudolf Friedrich
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Abstract

A new optimization procedure for the estimation of Kramers-Moyal coefficients from stationary, one-dimensional, Markovian time series data is presented. The method takes advantage of a recently reported approach that allows to calculate exact finite sampling interval effects by solving the adjoint Fokker-Planck equation. Therefore it is well suited for the analysis of sparsely sampled time series. The optimization can be performed either making a parametric ansatz for drift and diffusion functions or also parameter free. We demonstrate the power of the method in several numerical examples with synthetic time series.

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Christoph Honisch, Rudolf Friedrich. 2011-02-25. Estimation of Kramers-Moyal coefficients at low sampling rates. https://doi.org/10.1103/physreve.83.066701

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