发表机构
University of Silesia in Katowice; AGH University of Science and Technology（卡托维兹西里西亚大学; AGH科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对变换集与变换选择分布随时间变化的随机迭代函数系统，给出两类动力学下几何吸引概率测度的存在准则，并通过仿射变换模型验证结果。
AI 中文摘要
本文研究随机迭代函数系统的渐近行为，其中变换族及各步选择变换的分布均随时间变化。我们考虑两类动力学：由前向迭代产生的时非齐次马尔可夫链，以及由后向迭代生成的非马尔可夫过程。针对这两种情形，我们给出了概率测度的存在准则，该测度在有界利普希茨距离下呈几何吸引性，且与初始分布无关。最后，我们通过涉及仿射变换的特定模型的应用示例说明所得结果。
英文摘要
In this paper, we focus on the asymptotic behavior of random iterated functions systems, in which both the family of transformations and the distribution of selecting them vary at each step. We consider two types of dynamics: the time-inhomogeneous Markov chain arising from forward iterates and the non-Markovian process generated by backward iterates. For both settings, we provide certain criteria for the existence of a probability measure that is geometrically attracting in the bounded Lipschitz distance, independently of the initial distribution. Finally, we illustrate our results through applications to specific models involving affine transformations.
