Lade Steven J
Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Australian Capital Territory 0200, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031137. doi: 10.1103/PhysRevE.80.031137. Epub 2009 Sep 24.
Kramers-Moyal coefficients provide a simple and easily visualized method with which to analyze nonlinear stochastic time series. One mechanism that can affect the estimation of the coefficients is geometric projection effects. For some biologically inspired examples, these effects are predicted and explored with a nonstochastic projection operator method and compared with direct numerical simulation of the systems' Langevin equations. General features and characteristics are identified, and the utility of the Kramers-Moyal method is discussed. Projections of a system are in general non-Markovian, but here the Kramers-Moyal method remains useful, and in any case the primary examples considered are found to be close to Markovian.
克莱默斯-莫亚尔系数提供了一种简单且易于可视化的方法来分析非线性随机时间序列。一种会影响系数估计的机制是几何投影效应。对于一些受生物启发的例子，利用非随机投影算子方法预测并探究了这些效应，并与系统朗之万方程的直接数值模拟进行了比较。识别出了一般特征，并讨论了克莱默斯-莫亚尔方法的效用。系统的投影通常是非马尔可夫的，但在此克莱默斯-莫亚尔方法仍然有用，并且在任何情况下，所考虑的主要例子被发现都接近马尔可夫过程。
