具有位置相关概率的随机迭代

IF 0.4 4区 数学 Q4 STATISTICS & PROBABILITY
R. Kapica, M. Ślȩczka
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引用次数: 20

摘要

由函数$S_{\theta}:X\to X$, $\theta \in \Theta$随机迭代产生的马尔可夫链,其中$X$是波兰空间,$\Theta$是任意索引集。在$x\in X$上,$\theta$是从$\Theta$上的分布$\theta_x$中采样的,$\theta_x$对于不同的$x$是不同的。证明了指数收敛于唯一不变测度。该结果应用于${\mathbb R}^d$上随机仿射变换的情况,给出了具有位置相关概率的指数吸引永续的存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Random iteration with place dependent probabilities
Markov chains arising from random iteration of functions $S_{\theta}:X\to X$, $\theta \in \Theta$, where $X$ is a Polish space and $\Theta$ is arbitrary set of indices are considerd. At $x\in X$, $\theta$ is sampled from distribution $\theta_x$ on $\Theta$ and $\theta_x$ 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.
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来源期刊
CiteScore
0.70
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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