We consider systems of two specific piecewise linear homeomorphisms of the unit interval, so called the Alseda-Misiurewicz systems, and investigate the basic properties of Markov chains which arise when these two transformations are applied randomly with probabilities depending on the point of the interval. Though this iterated function system is not contracting in average and known methods do not apply, stability and the strong law of large numbers are proven.

中文翻译：

---

具有位置相关概率的 Alsedà–Misiurewicz 系统

我们考虑单位区间的两个特定分段线性同胚系统，即所谓的 Alseda-Misiurewicz 系统，并研究了马尔可夫链的基本性质，当这两个变换被随机应用时，概率取决于区间的点。虽然这个迭代函数系统不是平均收缩的，并且已知方法不适用，但证明了稳定性和强大的大数定律。