Beentjes Casper H L, Baker Ruth E
Mathematical Institute, University of Oxford, Oxford, United Kingdom.
J Chem Phys. 2019 Apr 21;150(15):154107. doi: 10.1063/1.5081043.
This work considers the method of uniformization for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformization can be beneficial in the context of time-inhomogeneous models, such as chemical reaction networks incorporating extrinsic noise. This paper lays focus on the understanding of uniformization from the viewpoint of sample paths of chemical reaction networks. In particular, an efficient pathwise stochastic simulation algorithm for time-homogeneous models is presented which is complexity-wise equal to Gillespie's direct method. This new approach therefore enlarges the class of problems for which the uniformization approach forms a computationally attractive choice. Furthermore, as a new application of the uniformization method, we provide a novel variance reduction method for (raw) moment estimators of chemical reaction networks based upon the combination of stratification and uniformization.
本文在化学反应网络的背景下考虑连续时间马尔可夫链的均匀化方法。文献中先前的工作表明，在非齐次模型（如包含外部噪声的化学反应网络）的背景下，均匀化可能是有益的。本文着重从化学反应网络样本路径的角度理解均匀化。特别地，提出了一种针对齐次模型的高效路径随机模拟算法，其在计算复杂度上与 Gillespie 直接方法相当。因此，这种新方法扩大了均匀化方法在计算上具有吸引力的问题类别。此外，作为均匀化方法的一种新应用，我们基于分层和均匀化的组合，为化学反应网络的（原始）矩估计提供了一种新颖的方差缩减方法。
