连续时间马尔可夫链的多层蒙特卡洛方法及其在生化动力学中的应用
Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics
AI总结：
本文通过将多层蒙特卡洛方法扩展到连续时间马尔可夫链，利用耦合技术降低计算复杂度，并构建无偏估计器，显著提高了计算效率。
摘要：
我们展示了如何将最近提出的多层蒙特卡洛方法扩展到连续时间马尔可夫链设置，从而大大降低了为达到指定精度计算系统状态函数期望值所需的计算复杂度。该扩展非平凡，利用了所需过程的耦合，易于模拟且估计量方差小。此外，与其他多层蒙特卡洛实现截然不同，我们展示了如何产生一个无偏估计器，其计算成本显著低于通常由精确算法结合原始蒙特卡洛得到的无偏估计器。因此，我们以可量化的方式显著改进了当前在科学文献中有许多名称和变体的基本计算复杂度，包括Bortz-Kalos-Lebowitz算法、离散事件模拟、动态蒙特卡洛、动力学蒙特卡洛、n-fold方式、下一反应方法、停留时间算法、随机模拟算法、Gillespie算法和tau-leaping。新算法具有通用性，但我们也给出了一个例子，其中仅耦合思想（即使没有多层离散化）也可通过利用系统结构来提高效率。随机建模的化学反应网络是这项工作非常重要的应用。因此，我们使用这一背景来设定符号、术语、自然缩放和计算示例。
英文摘要：
We show how to extend a recently proposed multi-level Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the system to a specified accuracy. The extension is non-trivial, exploiting a coupling of the requisite processes that is easy to simulate while providing a small variance for the estimator. Further, and in a stark departure from other implementations of multi-level Monte Carlo, we show how to produce an unbiased estimator that is significantly less computationally expensive than the usual unbiased estimator arising from exact algorithms in conjunction with crude Monte Carlo. We thereby dramatically improve, in a quantifiable manner, the basic computational complexity of current approaches that have many names and variants across the scientific literature, including the Bortz-Kalos-Lebowitz algorithm, discrete event simulation, dynamic Monte Carlo, kinetic Monte Carlo, the n-fold way, the next reaction method,the residence-time algorithm, the stochastic simulation algorithm, Gillespie's algorithm, and tau-leaping. The new algorithm applies generically, but we also give an example where the coupling idea alone, even without a multi-level discretization, can be used to improve efficiency by exploiting system structure. Stochastically modeled chemical reaction networks provide a very important application for this work. Hence, we use this context for our notation, terminology, natural scalings, and computational examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
