To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating states in a grid structure. The resulting approximate stationary distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection tailored to the stationary behavior. We demonstrate the method's applicability to a wide range of non-linear problems with complex stationary behaviors.

翻译：为了了解Markov人口模型的长期行为,计算固定分布往往是一个关键部分。我们建议采用基于脱轨的近似法,采用州-空整流法,将各州合并成一个网格结构。由此得出的近似固定分布法被用于迭接地完善国家-空间的相关部分,并疏离不相干的部分。这样算法就学会了一种与固定行为相适应的、合理合理的有限状态预测。我们展示了该方法对一系列非线性问题和复杂的固定行为的适用性。