早期停止定理在随机游动中的应用
The Application of the Early Stopping Theorem in Random Walk
DOI: 10.12677/PM.2021.1112226, PDF, HTML, 下载: 270  浏览: 1,513  科研立项经费支持
作者: 赵 盼：北京联合大学，数理与交叉科学研究院，北京
关键词: 随机游动；早期停止定理；强平稳对偶；随机控制；随机单调；Random Walk； The Early Stopping Theorem； Strong Stationary Duality； Stochastically Dominate； Stochastically Monotone
摘要: Diaconis 和 Fill 利用早期停止定理, 给出ℤ+上的随机游动收敛到平稳分布的速度估计时出现了错误，本文不仅纠正了这个错误，而且利用 Markov 不等式和早期停止定理，也给出了ℤ+上的随机游动收敛到平稳分布的速度估计。
Abstract: By using the early stopping theorem, Diaconis and Fill made a mistake when dealing with the convergence to stationarity for a random walk.  In the paper, we not only correct the mistake, but also give the speed estimation of convergence to stationarity for the random walk, by using the Markov inequation and the early stopping theorem.
文章引用：赵盼. 早期停止定理在随机游动中的应用[J]. 理论数学, 2021, 11(12): 2023-2030. https://doi.org/10.12677/PM.2021.1112226

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