中文摘要：

反应网络广泛存在于自然系统中.原理上,概率主方程对任何反应网络系统的随机行为提供了最为完整的数学模型.然而,分析和模拟这种类型的方程长期以来是一项挑战性任务.至目前为止,有关问题并没有得到根本解决,相关研究仍在继续.该文对概率主方程的研究进展进行了较为系统和全面的综述,聚焦于若干常用的近似分析方法（如线性噪声逼近、普通矩封闭法、2项矩方法等）与常用的数值方法（如Gillespie随机模拟算法、有限状态映射法、矩封闭格式等）.特别地,分析了概率主方程研究取得缓慢进展的主要原因,讨论并提出了可能的解决方案.

英文摘要：

Reaction networks exist extensively in natural systems. In principle,probability master equations provide the most complete models of probabilistic behavior for any reaction network systems. However,analysis and simulation of these equations have been a challenging task for a long time; these problems have not been thoroughly unsolved until now and relevant studies are still continuing. This article presents a systematic and comprehensive review on study of probability master equations,focusing on common theoretical analysis methods such as linear noise approximation,common moment-closure methods and binomial moment approach,and common numerical approaches such as Gillespie stochastic simulation approach,finite state mapping method and moment-closure formulations. In particular,some reasons why slow progress is made in study of probability master equations are analyzed,and possible schemes for solving probability master equations are discussed and suggested.