论文标题
M/g/1型马尔可夫链的水平截断近似的水平尺寸收敛
Level-wise Subgeometric Convergence of the Level-increment Truncation Approximation of M/G/1-type Markov Chains
论文作者
论文摘要
本文考虑了M/G/1型马尔可夫链的水平提示（LI）截断近似。 LI截断近似可用于实现M/G/1范式，这是计算M/G/1型Markov链的固定分布的框架。本文的主要结果是用于原始固定分布与其LI截断近似之间的总变化距离的子几何收敛公式。假设平衡水平插入分布是次指数的，并且向下跃迁矩阵是等级的。然后，我们表明，LI截断近似的总变异误差的收敛速率等于平衡水平收入分布的尾部和原始固定分布的尾部的收敛率。
This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is useful for implementing the M/G/1 paradigm, which is the framework for computing the stationary distribution of M/G/1-type Markov chains. The main result of this paper is a subgeometric convergence formula for the total variation distance between the original stationary distribution and its LI truncation approximation. Suppose that the equilibrium level-increment distribution is subexponential, and that the downward transition matrix is rank one. We then show that the convergence rate of the total variation error of the LI truncation approximation is equal to that of the tail of the equilibrium level-increment distribution and that of the tail of the original stationary distribution.
