标题： 一般生灭化学扩散主方程的解公式 显示英文标题

标题： Solution formula for the general birth-death chemical diffusion master equation

摘要： 我们为生灭型化学扩散主方程提出一个解公式。 这些方程在最近的论文[5]中被提出和形式化，旨在将分子的空间扩散纳入经典化学主方程所提供的描述中。 我们从[20]中开发的一般方法出发，并对其中找到的表示进行了更详细的分析。 这导致了一个生灭型化学扩散主方程的解公式，该公式用与所研究系统相关的反应扩散偏微分方程的解来表示。 这种表示还揭示了与经典生灭型化学主方程解之间的显著类比。 我们的发现的解也通过几个示例进行了说明。 显示英文摘要

摘要： We propose a solution formula for chemical diffusion master equations of birth and death type. These equations, proposed and formalized in the recent paper [5], aim at incorporating the spatial diffusion of molecules into the description provided by the classical chemical master equation. We start from the general approach developed in [20] and perform a more detailed analysis of the representation found there. This leads to a solution formula for birth-death chemical diffusion master equations which is expressed in terms of the solution to the reaction-diffusion partial differential equation associated with the system under investigation. Such representation also reveals a striking analogy with the solution to the classical birth-death chemical master equations. The solutions of our findings are also illustrated for several examples.