多尺度连续时间马尔可夫链中使用并行复制动力学的平稳平均
Stationary averaging for multi-scale continuous time Markov chains using parallel replica dynamics
AI总结：
本文提出两种算法用于模拟存在稳态的连续时间马尔可夫链，通过并行计算高效探索稳态集，无需假设可逆性，通过数值模拟验证方法一致性与效率。
摘要：
我们提出两种算法用于模拟存在稳态的连续时间马尔可夫链。我们证明在平稳性假设下，这些算法能正确估计过程的平稳平均。两种算法基于并行复制方法的思想，利用并行计算更高效地探索稳态集。算法仅需平稳性和可识别稳态的存在作为假设。特别地，不假设可逆性。为简化算法示例，本文假设整个论文中使用同步架构。我们提供了误差分析以及在多尺度随机反应网络模型上的数值模拟，以展示方法的一致性和效率。
英文摘要：
We propose two algorithms for simulating continuous time Markov chains in the presence of metastability. We show that the algorithms correctly estimate, under the ergodicity assumption, stationary averages of the process. Both algorithms, based on the idea of the parallel replica method, use parallel computing in order to explore metastable sets more efficiently. The algorithms require no assumptions on the Markov chains beyond ergodicity and the presence of identifiable metastability. In particular, there is no assumption on reversibility. For simpler illustration of the algorithms, we assume that a synchronous architecture is used throughout of the paper. We present error analyses, as well as numerical simulations on multi-scale stochastic reaction network models in order to demonstrate consistency of the method and its efficiency.
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