具有弱收缩性质的随机动力系统（有一章是Martin Benda的结果）
Stochastic dynamical systems with weak contractivity properties (with a chapter featuring results of Martin Benda)
摘要：
考虑一个真度量空间X和一个独立同分布序列。从X到X的随机连续映射F_n。在X中从x处导出随机动力系统（SDS）X_n^x = F_n（X_{n-1} ^x）.本文研究了不变测度的存在性、唯一性以及该过程的常返性和遍历性。在第一部分中，我们详细阐述，改进和完善了未发表的工作，马丁Benda的局部收缩性，值得宣传，并提供了一个重要的工具，研究随机迭代。我们考虑了F_n为压缩函数的情形，特别讨论了反射随机游动的常返准则及其锐度。在第二部分中，我们考虑了F_n为Lipschitz映射的情形。主要结果涉及的情况下，当相关的Lipschitz常数是对数中心。主要工具是Chacon-Ornstein定理和空间X的双曲扩张以及过程（X_n^x）。将所得结果应用于非负半直线上的反射仿射随机递推问题。
英文摘要：
Consider a proper metric space X and a sequence of i.i.d. random continuous mappings F_n from X to X. It induces the stochastic dynamical system (SDS) X_n^x = F_n(X_{n-1}^x) starting at x in X. In this paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying stochastic iterations. We consider the case when the F_n are contractions and, in particular, discuss recurrence criteria and their sharpness for reflected random walk. In the second part, we consider the case where the F_n are Lipschitz mappings. The main results concern the case when the associated Lipschitz constants are log-centered. Prinicpal tools are the Chacon-Ornstein theorem and a hyperbolic extension of the space X as well as the process (X_n^x). The results are applied to the reflected affine stochastic recursion on the non-negative half-line.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
