论文标题
马尔可夫操作员共同体的混合和观察
Mixing and observation for Markov operator cocycles
论文作者
论文摘要
我们考虑了Markov Operator Cocycles的随机动力学系统的混合和精确性定义。鉴于观察到环境中的随机性，我们首先给出了六个基本的Markov Operator Cocycles混合定义，并表明它们可以将其简化为两个不同的组。其次，我们给出了马尔可夫操作员Cocycles精确性的定义，并表明Lin的精确性标准可以自然扩展到Markov Operator Cocycles的情况。最后，在渐近周期性的马尔可夫操作员共同体中，我们显示了混合，精确性和渐近稳定性之间的lasota-mackey型等效性。
We consider generalized definitions of mixing and exactness for random dynamical systems in terms of Markov operator cocycles. We first give six fundamental definitions of mixing for Markov operator cocycles in view of observations of the randomness in environments, and show that they can be reduced into two different groups. Secondly, we give the definition of exactness for Markov operator cocycles and show that Lin's criterion for exactness can be naturally extended to the case of Markov operator cocycles. Finally, in the class of asymptotically periodic Markov operator cocycles, we show the Lasota-Mackey type equivalence between mixing, exactness and asymptotic stability.
