随机反应动力学的混合模拟方法
On hybrid simulation schemes for stochastic reaction dynamics
摘要：
化学反应网络的随机模拟的现有文献有一种趋势，尽可能快地移动到抽象的随机动力学的概率的基础上的化学主方程（CME）的概念，在很大程度上忽略了样本路径表示。在本出版物中，我们讨论的理论基础和数值方法的问题，在这一领域使用样本路径方法作为一个重要组成部分的过程。由于它依赖于一个弱解的随机微分方程系统的泊松随机措施驱动的基本随机过程的表示，这种方法带来承担迄今为止被忽视，但相当有效的解决问题的方法。首先，我们提出了一个简单而直观的方式划分物种和反应的相互作用网络到不同的群体。然后，我们讨论如何原来的随机动力学与状态依赖的强度的过渡可以重新制定的跳跃扩散随机微分方程驱动的维纳噪声源和泊松随机措施。最后，我们表明，这种方法有利于建设的混合仿真技术，在创建有效的技术建模的反应网络的多尺度随机动力学的重要一步。用简单直观的例子说明了从泊松随机测度中抽样事件的数值方法。对有限差分格式进行了差错控制分析。
英文摘要：
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.
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。
