When the state space of a discrete state space positive recurrent Markov chain is infinite or very large, it becomes necessary to truncate the state space in order to facilitate numerical computation of the stationary distribution. This paper develops a new approach for bounding the truncation error that arises when computing approximations to the stationary distribution. This rigorous a posteriori error bound exploits the regenerative structure of the chain and assumes knowledge of a Lyapunov function. Because the bound is a posteriori (and leverages the computations done to calculate the stationary distribution itself), it tends to be much tighter than a priori bounds. The bound decomposes the regenerative cycle into a random number of excursions from a set $K$ defined in terms of the Lyapunov function into the complement of the truncation set $A$. The bound can be easily computed, and does not (for example) involve a linear program, as do some other error bounds.

翻译：当离散状态空间正常返马尔可夫链的状态空间为无限或规模极大时，为便于平稳分布的数值计算，必须对状态空间进行截断。本文提出了一种新方法，用于界定在计算平稳分布近似值时产生的截断误差。该严格的后验误差界利用了链的再生结构，并假设已知一个李雅普诺夫函数。由于该界是后验的（并利用了计算平稳分布本身所进行的运算），其通常比先验界更为紧致。该误差界将再生循环分解为从由李雅普诺夫函数定义的集合$K$出发、进入截断集$A$的补集的随机数次游程。此误差界易于计算，且不涉及（例如）如其他某些误差界所需的线性规划。