随机演化环境中隐马尔可夫链的随机控制及其在接触过程中的应用
Stochastic domination for a hidden Markov chain with applications to the contact process in a randomly evolving environment
摘要：
普通的接触过程用于模拟疾病在人群中的传播。在这个模型中，每个受感染的个体在变得健康之前等待参数为1的指数分布时间。本文引入并研究了随机演化环境中的接触过程。在这里，我们将每个个体关联到独立的双状态$\{0,1\},$后台进程。给定$δ_0<δ_1,$，如果背景过程处于状态$0,$，则个体（如果被感染）以$δ_0,$的速率变得健康，而如果背景过程处于状态$1,$，则以$δ_1.$的速率变得健康。通过随机比较随机演化环境中的接触过程与普通接触过程，我们将研究灭绝以及弱生存和强生存的问题。在我们的分析中的一个关键步骤是获得某些点过程之间的随机控制结果。我们这样做是从一个离散的设置开始，然后采取连续的时间限制。
英文摘要：
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and study the contact process in a randomly evolving environment. Here we associate to every individual an independent two-state, $\{0,1\},$ background process. Given $δ_0<δ_1,$ if the background process is in state $0,$ the individual (if infected) becomes healthy at rate $δ_0,$ while if the background process is in state $1,$ it becomes healthy at rate $δ_1.$ By stochastically comparing the contact process in a randomly evolving environment to the ordinary contact process, we will investigate matters of extinction and that of weak and strong survival. A key step in our analysis is to obtain stochastic domination results between certain point processes. We do this by starting out in a discrete setting and then taking continuous time limits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
