Quantitative Coarse-Graining of Markov Chains
Quantitative Coarse-Graining of Markov Chains
复制标题
马尔可夫链的定量粗粒度化
DOI：
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发表时间：
2022
影响因子：
2
通讯作者：
U. Sharma
中科院分区：
文献类型：
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作者：
Bastian Hilder;U. Sharma
粗粒度技术在降低随机模型的复杂性方面发挥着核心作用，并且通常以将系统的完整状态投影到捕获系统基本特征的较小变量集上的映射为特征。从一个连续时间马尔可夫链开始，在这项工作中，我们提出并分析了一个有效的动力学，它近似的粗粒度链的动力学信息。在不假设明确的尺度分离，我们提供了充分的条件下，这种有效的动态保持接近原系统，并提供定量的近似误差的界限。我们还比较了有效的动态和相应的误差界平均文献马尔可夫链，涉及明确的尺度分离。我们证明了我们的研究结果的一个说明性的测试例子。
Coarse-graining techniques play a central role in reducing the complexity of stochastic models, and are typically characterised by a mapping which projects the full state of the system onto a smaller set of variables which captures the essential features of the system. Starting with a continuous-time Markov chain, in this work we propose and analyse an effective dynamics, which approximates the dynamical information in the coarse-grained chain. Without assuming explicit scale-separation, we provide sufficient conditions under which this effective dynamics stays close to the original system and provide quantitative bounds on the approximation error. We also compare the effective dynamics and corresponding error bounds to the averaging literature on Markov chains which involve explicit scale-separation. We demonstrate our findings on an illustrative test example.