关于M-V模型的遍历域

本文利用耦合的技巧,建立了接触过程与 M-V 模型的联系.由此将 d 维 M-V 模型的遍历域,由δ∈(d/(2d+1),(2d+1)/(4d))扩展到δ∈((2d-1)/(4d),(2d+1)/(4d)).特别当 d=1时,将其遍历域由(0,3/4)扩大到(0,0.78).这些均推广了[1]中的结果.     

The ergodicity of stochastic partial differential equations with Lévy jump

In this article, the authors prove the uniqueness in law of a class of stochastic equations in infinite dimension, then we apply it to establish the existence and uniqueness of invariant measure of the generalized stochastic partial differential equation perturbed by Lévy process.     

广义算子半群的遍历及概率逼近定理

首先给出了广义算子半群的Abel-遍历和Cesaro-遍历的定义,对两种遍历的性质进行了刻画,研究了两种遍历的等价条件.其次,利用Pettis积分、算子值数学期望及广义连续修正模等工具给出广义算子半群的概率逼近表达式.     

遍历定理的应用--一类极限的求法

作为遍历理论的应用,讨论一类极限的求法.     

比较判别法在泛函分析中的应用

在数学分析中,比较判别法是判断正项级数收敛性的一种基础的方法.借鉴比较判别法的思想,应用于泛函分析中用来判别p次可和序列空间上的加权移位算子是否为Cesàro有界的或绝对Cesàro有界的.     

f-ergodicity of Markov Process by Coupling Method北大核心CSCD

We first study the basic coupling and obtain an equation between total variation norm and the basic coupling. Then by use this equation we investigate the ergodicity property of continuous time Markov processes in general state space. For an ergodic continuous-time Markov processes, adding condition π(f) < ∞, by using the coupling method, there exists the full absorption set, such that the continuous time Markov processes are f-ergodic on it. © 2022 Chinese Academy of Sciences. All rights reserved.     

带有隔离的COVID-19随机SQIR模型研究

本文考虑一类受环境噪声影响,带有隔离的COVID-19随机SQIR传染病模型.通过构造Lyapunov函数并利用It?公式,证明全局正解的存在唯一性;得到决定疾病灭绝、持久和遍历平稳分布的充分条件.结果表明:环境变化在一定条件下会对疾病起抑制作用.最后,通过数值模拟来验证理论结果的正确性.