In this paper, we consider absorbing Markov chains $X_n$ admitting a quasi-stationary measure $\mu $ on M where the transition kernel ${\mathcal P}$ admits an eigenfunction $0\leq \eta \in L^1(M,\mu )$ . We find conditions on the transition densities of ${\mathcal P}$ with respect to $\mu $ which ensure that $\eta (x) \mu (\mathrm {d} x)$ is a quasi-ergodic measure for $X_n$ and that the Yaglom limit converges to the quasi-stationary measure $\mu $ -almost surely. We apply this result to the random logistic map $X_{n+1} = \omega _n X_n (1-X_n)$ absorbed at ${\mathbb R} \setminus [0,1],$ where $\omega _n$ is an independent and identically distributed sequence of random variables uniformly distributed in $[a,b],$ for $1\leq a <4$ and $b>4.$

中文翻译：

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关于具有无界转移密度的吸收马尔可夫链的拟遍历性，包括带有逃逸的随机逻辑映射

在本文中，我们考虑吸收马尔可夫链 $X_n$ 承认准稳态测度 $\亩$ 在中号其中转换内核 ${\数学P}$ 承认本征函数 $0\leq \eta \in L^1(M,\mu )$ 。我们找到了转变密度的条件 ${\数学P}$ 关于 $\亩$ 这确保了 $\eta (x) \mu (\mathrm {d} x)$ 是一个准遍历测度 $X_n$ 并且 Yaglom 极限收敛于准稳态测度 $\亩$ ——几乎可以肯定。我们将此结果应用于随机逻辑图 $X_{n+1} = \omega _n X_n (1-X_n)$ 吸收于 ${\mathbb R} \setminus [0,1],$ 在哪里 $\omega_n$ 是均匀分布的随机变量的独立同分布序列 $[a,b],$ 为了 $1\leq a <4$ 和 $b>4.$