标题： 概率推导与分析带有相互湮灭的化学扩散主方程 显示英文标题

标题： Probabilistic derivation and analysis of the chemical diffusion master equation with mutual annihilation

摘要： 我们提出了一种概率推导方法，用于所谓的化学扩散主方程（CDME），并描述了一种无限维矩生成函数方法，以找到其解析解。 CDME通过一个无限耦合的Fokker-Planck方程系统来模拟与单个粒子空间扩散相关的化学反应动力学的概率演化；在此，我们关注的是创建和相互湮灭化学反应，以及单个粒子的布朗扩散。 我们的概率方法模仿了出生-死亡连续时间马尔可夫链的后向Kolmogorov方程的推导。 此外，所提出的无限维矩生成函数方法将CDME解的某些有限维投影与包含与上述投影空间维度相同变量的单个线性四阶偏微分方程的解联系起来。 显示英文摘要

摘要： We propose a probabilistic derivation of the so-called chemical diffusion master equation (CDME) and describe an infinite dimensional moment generating function method for finding its analytical solution. CDMEs model by means of an infinite system of coupled Fokker-Planck equations the probabilistic evolution of chemical reaction kinetics associated with spatial diffusion of individual particles; here, we focus an creation and mutual annihilation chemical reactions combined with Brownian diffusion of the single particles. Our probabilistic approach mimics the derivation of backward Kolmogorov equations for birth-death continuous time Markov chains. Moreover, the proposed infinite dimensional moment generating function method links certain finite dimensional projections of the solution of the CDME to the solution of a single linear fourth order partial differential equation containing as many variables as the dimension of the aforementioned projection space.