论文标题
关于截断方案的收敛，用于近似连续状态空间马尔可夫链和过程的固定分布
On Convergence of a Truncation Scheme for Approximating Stationary Distributions of Continuous State Space Markov Chains and Processes
论文作者
论文摘要
在对马尔可夫链条和过程的分析中，有时用“截断”有界状态空间替换无界状态空间很方便。当进行这种替换时，人们经常想知道截短链或过程的平衡行为是否接近未截断系统的平衡行为。例如，当考虑用于计算无限状态空间上固定分布的数值方法时，这些问题自然会出现。在本文中，我们使用“再生”的原理表明，当未截断的链条是阳性harris harris recurrent时，“固定状态”截断的固定分布以很大的一般性（总变异规范）收敛到未截断极限的固定分布。即使在可数的状态空间中，我们的理论也通过表明增强可以对应于$ r $ to的度量来扩展已知的结果。此外，我们将理论扩展为涵盖Harris重复的马尔可夫过程的重要子类，其中包括非爆炸马尔可夫跳跃过程。
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior of the truncated chain or process is close to that of the untruncated system. For example, such questions arise naturally when considering numerical methods for computing stationary distributions on unbounded state space. In this paper, we use the principle of "regeneration" to show that the stationary distributions of "fixed state" truncations converge in great generality (in total variation norm) to the stationary distribution of the untruncated limit, when the untruncated chain is positive Harris recurrent. Even in countable state space, our theory extends known results by showing that the augmentation can correspond to an $r$-regular measure. In addition, we extend our theory to cover an important subclass of Harris recurrent Markov processes that include non-explosive Markov jump processes on countable state space.
