标题： 随机动力系统，熵和信息 显示英文标题

标题： Random dynamical systems, entropies and information

摘要： 事件预测是许多不同学科中的挑战，从气象学到金融学；这个任务越困难，系统就越{\it 复数}。 然而，即使根据这个有限的定义，关于什么是复杂性的正确指标仍没有达成普遍共识。 特别是，对于那些时间演化受不受控制的因素影响，并表现为随机参数或随机噪声的系统，这种特征仍然缺乏。 本文展示了如何在信息论的背景下找到复杂性的正确指标。 关键点在于，答案取决于随机参数是否可测量，这有两种情况。 这个看似简单的观察内容在文献中经常被忽视，导致了矛盾的结果。 当随机参数可测量时，可预测性显然更大，然而，在相反的情况下，当未知的随机参数存在时间相关性时，可预测性会得到改善。 显示英文摘要

摘要： Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general consensus on what should be the correct indicator for complexity is still not reached. In particular, this characterization is still lacking for systems whose time evolution is influenced by factors which are not under control and appear as random parameters or random noise. We show in this paper how to find the correct indicators for complexity in the information theory context. The crucial point is that the answer is twofold depending on the fact that the random parameters are measurable or not. The content of this apparently trivial observation has been often ignored in literature leading to paradoxical results. Predictability is obviously larger when the random parameters are measurable, nevertheless, in the contrary case, predictability improves when the unknown random parameters are time correlated.