论文标题
两类随机建模的反应网络的混合时间
Mixing times for two classes of stochastically modeled reaction networks
论文作者
论文摘要
过去几十年来，人们对关于随机建模反应网络的固定分布的存在，形式和特性的问题进行了强有力的研究。当随机模型接收固定分布时，一个重要的实际问题是：该过程分布到固定分布的分布的收敛速率是多少？除了\ cite {xuhansenwiuf2022}与状态空间仅限于非阴性整数的模型有关的{xuhansenwiuf2022}，在反应网络文献中，与这种收敛速率相关的结果很明显。本文开始了在我们理解中填补这个洞的过程。在本文中，我们针对两类随机建模的反应网络的混合时间来表征这种收敛速率。具体而言，通过应用福斯特 - 裂解标准，我们为在\ cite {anderson2018some}中引入的两个反应网络建立了指数性构想。此外，我们表明，对于其中一个类，收敛性在初始状态上是统一的。
The past few decades have seen robust research on questions regarding the existence, form, and properties of stationary distributions of stochastically modeled reaction networks. When a stochastic model admits a stationary distribution an important practical question is: what is the rate of convergence of the distribution of the process to the stationary distribution? With the exception of \cite{XuHansenWiuf2022} pertaining to models whose state space is restricted to the non-negative integers, there has been a notable lack of results related to this rate of convergence in the reaction network literature. This paper begins the process of filling that hole in our understanding. In this paper, we characterize this rate of convergence, via the mixing times of the processes, for two classes of stochastically modeled reaction networks. Specifically, by applying a Foster-Lyapunov criteria we establish exponential ergodicity for two classes of reaction networks introduced in \cite{anderson2018some}. Moreover, we show that for one of the classes the convergence is uniform over the initial state.
