马尔可夫链集结及其在组合反应网络中的应用
Markov chain aggregation and its applications to combinatorial reaction networks
摘要：
我们考虑一个连续时间马尔可夫链（CTMC），其状态空间被划分为聚集，每个聚集被分配一个概率测度。作为弱集块性的一个变体，给出了在集块上定义CTMC的一个充分条件，该条件也刻画了原过程的测度可以从集块测度中恢复.我们展示了解聚集的适用性如何依赖于初始分布。应用部分是文章的一个主要方面，在那里我们说明了随机规则为基础的模型，生化反应网络形成了一个重要的领域，使用的工具，在文件中开发的。对于基于规则的模型，聚集体的构造和聚集体上的分布的计算是算法的。在三个案例研究中举例说明了这些技术。
英文摘要：
We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is a major aspect of the article, where we illustrate that the stochastic rule-based models for biochemical reaction networks form an important area for usage of the tools developed in the paper. For the rule-based models, the construction of the aggregates and computation of the distribution over the aggregates are algorithmic. The techniques are exemplified in three case studies.
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