连续时间的熵
Entropies in case of continuous time
摘要：
在时间序列分析的框架中的时间离散设置的信息理论推广到时间连续的情况下。考虑Roessler和Lorenz动力学以及Ornstein-Uhlenbeck过程产生的时间连续熵的混沌和噪声的区别的一种新的可能性。在确定性的情况下，在无限高的采样率的限制下的联合不确定性的上限阈值可以被发现，并且熵率可以被计算为熵的通常的时间导数。在三维表示的联合熵的空间分辨率，离散化时间步长和不确定性评估时间的依赖性显示在一个统一的方式。因此，任何动力学的维数和柯尔莫哥洛夫-西奈熵率都可以作为极限情况从一个图中读出。
英文摘要：
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for time-continuous entropies a new possibility for the distinction of chaos and noise. In the deterministic case an upper threshold of the joint uncertainty in the limit of infinitely high sampling rate can be found and the entropy rate can be calculated as a usual time derivative of the entropy. In a three-dimensional representation the dependence of the joint entropy on space resolution, discretization time step length and uncertainty-assessed time is shown in a unified manner. Hence the dimension and the Kolmogorov-Sinai entropy rate of any dynamics can be read out as limit cases from one single graph.
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