标题： 关于随机反应动力学的混合模拟方案 显示英文标题

标题： On hybrid simulation schemes for stochastic reaction dynamics

摘要： 现有关于化学反应网络随机模拟的文献倾向于尽可能快地转向基于化学主方程（CME）概念的概率形式的随机动力学抽象表述，而很大程度上忽略了样本路径表示。 在本出版物中，我们使用样本路径方法作为过程的关键部分，讨论该领域问题的理论基础和数值方法。 由于它依赖于将底层随机过程表示为由泊松随机测度驱动的随机微分方程系统的弱解，这种方法引入了一种此前被忽视但非常有效的解决问题的方法。 我们首先介绍一种简单且直观的方式，将相互作用网络中的物种和反应分为不同的组。 然后我们讨论如何将具有状态依赖转移强度的原始随机动力学重新表述为由维纳噪声源和泊松随机测度驱动的跳跃扩散随机微分方程。 最后，我们表明这种方法有助于构建混合模拟技术，这是创建用于模拟反应网络多尺度随机动力学的有效技术的重要步骤。 与从泊松随机测度中采样事件相关的数值方法在简单直观的例子中得到演示。 还提供了有限差分方案的误差控制分析。 显示英文摘要

摘要： The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the Chemical Master Equation (CME), largely ignoring sample path representation. In this publication we discuss both theoretical basis and numerical approach for the problems in this area using sample path methods as a crucial part of the process. Relying as it does on a representation of the underlying stochastic processes as a weak solution of a system of stochastic differential equations driven by Poisson random measures this approach brings to bear a heretofore ignored but quite effective problem solving methodology. We first present a simple and intuitive way of partitioning species and reactions of the interaction network into different groups. We then discuss how original stochastic dynamics with state dependent intensities of transitions can be reformulated in terms of jump-diffusion stochastic differential equations driven by both Wiener noise sources and Poisson random measures. Finally, we show that this approach facilitates the construction of hybrid simulation techniques, an important step in the creation of efficient techniques for modeling multi-scale stochastic dynamics of the reaction networks. Numerical methods related to sampling events from Poisson random measures are demonstratedon simple intuitive examples. Error control analysis of the finite differences scheme is also presented.