In this paper, we study the speed of mixing of absorbing Markov processes with state space $E$, that is, the rate of the convergence in the following limits: $\underset{t\to \infty }{lim}{\mathbb{E}}_x\left[f\left(X_{pt}\right)g\left(X_t\right)\right|T>t]={\int }_{E}f\left(y\right)\beta \left(dy\right){\int }_{E}g\left(y\right)\alpha \left(dy\right),$ $\underset{t\to \infty }{lim}{\mathbb{E}}_x\left[f\left(X_{pt}\right)g\left(X_{qt}\right)\right|T>t]={\int }_{E}f\left(y\right)\beta \left(dy\right){\int }_{E}g\left(y\right)\beta \left(dy\right),$where $f,g$ are bounded and measurable functions defined on $E$, $x\in E$, $0<p<q<1$, $T$ is the absorption time of the process, $\alpha$ is a quasi-stationary distribution and $\beta$ is a quasi-ergodic distribution. Under general conditions, we show that the convergence rates of the limits are exponential. As an application, we apply our result to the logistic Feller diffusion process and the birth–death process with catastrophes.

在本文中，我们研究了吸收马尔可夫过程与状态空间的混合速度 $乙$，即收敛速度在以下限制中： $\underset{吨\to \infty }{林}{\mathbb{乙}}_X\left[F\left(X_{磷吨}\right)G\left(X_{吨}\right)\right|吨>吨]={\int }_{乙}F\left(是\right)\beta \left(d是\right){\int }_{乙}G\left(是\right)\alpha \left(d是\right),$ $\underset{吨\to \infty }{林}{\mathbb{乙}}_X\left[F\left(X_{磷吨}\right)G\left(X_{q吨}\right)\right|吨>吨]={\int }_{乙}F\left(是\right)\beta \left(d是\right){\int }_{乙}G\left(是\right)\beta \left(d是\right),$在哪里 $F,G$ 是定义在上的有界和可测量的函数 $乙$, $X\in 乙$, $0<磷<q<1$, $吨$ 是过程的吸收时间， $\alpha$ 是准平稳分布，且 $\beta$是准遍历分布。在一般条件下，我们表明极限的收敛速度是指数的。作为一个应用，我们将我们的结果应用于逻辑费勒扩散过程和具有灾难的生死过程。