位置相关概率的随机迭代
Random iteration with place dependent probabilities
摘要：
本文研究了由函数$S_θ:X\to X$，$θ\in Θ$随机迭代产生的马氏链，其中$X$是Polish空间，$Θ$是任意指数集.在$x\in X$，$θ$从$Θ$上的分布$θ_x$中采样，并且对于不同的$x$，$θ_x$不同。证明了算法指数收敛于一个唯一不变测度。这一结果适用于随机仿射变换的情况下，${\mathbb R}^d$给出存在指数吸引的永久性与地方相关的概率。
英文摘要：
Markov chains arising from random iteration of functions $S_θ:X\to X$, $θ\in Θ$, where $X$ is a Polish space and $Θ$ is arbitrary set of indices are considerd. At $x\in X$, $θ$ is sampled from distribution $θ_x$ on $Θ$ and $θ_x$ are different for different $x$. Exponential convergence to a unique invariant measure is proved. This result is applied to case of random affine transformations on ${\mathbb R}^d$ giving existence of exponentially attractive perpetuities with place dependent probabilities.
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。
