论文标题
渐近周期性的超均匀马尔可夫进程的奇异定理，并应用于准平台，并具有移动边界
An ergodic theorem for asymptotically periodic time-inhomogeneous Markov processes, with application to quasi-stationarity with moving boundaries
论文作者
论文摘要
本文介绍了特定时间偶然的马尔可夫过程的基础定理，其时间均匀性是渐近的周期性的。在Lyapunov/次要条件下，可以表明，对于任何可测量的有限函数$ f $，平均时间$ \ frac {1} {t} {t} \ int_0^t f（x_s）ds $收敛于$ \ mathbb {l}^2 $中的限制性分布，从任何初始分布开始，从任何初始分布到$（x__t）$（x__t）。在初始度量的附加假设下，可以将这种收敛提高到几乎确定的收敛。然后将应用该结果以显示由渐近周期性移动边界吸收的过程的准分布的存在，从而满足有条件的多丁氏蛋白的状况。
This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose the time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded function $f$, the time average $\frac{1}{t} \int_0^t f(X_s)ds$ converges in $\mathbb{L}^2$ towards a limiting distribution, starting from any initial distribution for the process $(X_t)_{t \geq 0}$. This convergence can be improved to an almost sure convergence under an additional assumption on the initial measure. This result will be then applied to show the existence of a quasi-ergodic distribution for processes absorbed by an asymptotically periodic moving boundary, satisfying a conditional Doeblin's condition.
