Honisch Christoph, Friedrich Rudolf
Institute for Theoretical Physics, University of Muenster, D-48149 Muenster, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066701. doi: 10.1103/PhysRevE.83.066701. Epub 2011 Jun 6.
An 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 one 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 by making a parametric ansatz for drift and diffusion functions or parameter free. We demonstrate the power of the method in several numerical examples with synthetic time series.
提出了一种从平稳的一维马尔可夫时间序列数据估计克莱默斯-莫亚尔系数的优化程序。该方法利用了最近报道的一种方法，该方法允许通过求解伴随福克-普朗克方程来计算精确的有限采样间隔效应。因此，它非常适合于分析稀疏采样的时间序列。优化可以通过对漂移和扩散函数进行参数假设或无参数来进行。我们在几个合成时间序列的数值例子中展示了该方法的威力。
