本文是一篇关于可数马氏链截断扩充逼近算法的综述性文章.截断扩充逼近算法是研究可数无限马氏链的一个有效的方法.它已经成为计算马氏链的平稳分布以及其他参数的关键性工具.本文首先应用截断扩充逼近算法对平稳分布进行研究.我们利用遍历方法以及扰动方法,分别给出在全变差范数意义下以及在V范数意义下的平稳分布的收敛性和误差界.其次,本文应用截断扩充逼近算法研究泊松方程的解.我们给出泊松方程的解的收敛性质,并且考虑中心极限定理中偏差常数的逼近算法.此外,我们将用一些实际的例子来验证这些结果的实用性与准确性.最后,本文对截断扩充逼近算法的一些延伸问题进行了总结与展望.“,”In this paper,we present a survey of the technique of augmented truncation approximation for countable Markov chains.The augmented truncation approximation is a useful method to investigate infinite Markov chains,which is usually used to calculate the stationary distribution and other important parameters for Markov chains.Here we first apply the augmented truncation approximation to study the stationary distribution.We adopt the ergodicity method and the perturbation method to investigate the convergence and error bounds in terms of the total variation norm and the V-norm,respectively.Then,we discuss the augmented truncation approximations of the solution of Poisson\'s equation.The convergence to the solution is studied and the truncation approximations to the variance con-stant in central limit theorems are also considered.These results are illustrated through several examples.Finally pos-sible extensions are discussed in concluding remarks.