tau-leap 模拟方法的误差分析
Error analysis of tau-leap simulation methods
AI总结：
本文在时间离散化步长与系统状态范数的某有界幂次成反比的尺度下，对连续时间马尔可夫链的数值逼近方法进行误差分析，证明中点 tau-leap 在弱和强意义上均比欧拉 tau-leap 具有更高精度。
摘要：
我们对化学和生物化学文献中常见的连续时间马尔可夫链模型的数值逼近方法进行误差分析。分析的目的是能够比较不同逼近方法的精度，特别是欧拉 tau-leap 和中点 tau-leap。我们在时间离散化步长与系统状态范数的某有界幂次成反比的尺度下进行分析。我们认为这比先前误差分析中时间离散化步长独立于模型其余部分趋于零的尺度更合适。在当前尺度下，我们证明中点 tau-leap 在弱和强意义上均比欧拉 tau-leap 具有更高的精度；这一结果与先前的分析相反。我们给出示例来展示我们的发现。
英文摘要：
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the time discretization is inversely proportional to some (bounded) power of the norm of the state of the system. We argue that this is a more appropriate scaling than that found in previous error analyses in which the size of the time discretization goes to zero independent of the rest of the model. Under the present scaling, we show that midpoint tau-leaping achieves a higher order of accuracy, in both a weak and a strong sense, than Euler tau-leaping; a result that is in contrast to previous analyses. We present examples that demonstrate our findings.
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