论文标题
关于吸收带有无限过渡密度的马尔可夫链的准凝胶，包括随机的逻辑图和逃生
On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape
论文作者
论文摘要
在本文中，我们考虑吸收马尔可夫链$ x_n $承认$ m $上的准平台度量$μ$，其中过渡核$ \ mathcal p $允许eigenfunction $ 0 \ leq punction $ 0 \ leqη\ in L^1（m，m，μ）$。我们发现相对于$μ$的$ \ MATHCAL P $的过渡密度的条件，这确保$η（x）μ（\ Mathrm d x）$是$ x_n $的准方法，并且yaglom limim Limit convers the quasi-stationary stitationary Mesuary $μ$ $ $ $ $ $ - 最多。我们将此结果应用于随机逻辑映射$ x_ {n+1} =ω_nx_n（1-x_n）$在$ \ Mathbb r \ setMinus [0,1]，$ ch $ω_n$是I.I.D setminus [0,1]中
In this paper, we consider absorbing Markov chains $X_n$ admitting a quasi-stationary measure $μ$ on $M$ where the transition kernel $\mathcal P$ admits an eigenfunction $0\leq η\in L^1(M,μ)$. We find conditions on the transition densities of $\mathcal P$ with respect to $μ$ which ensure that $η(x) μ(\mathrm d x)$ is a quasi-ergodic measure for $X_n$ and that the Yaglom limit converges to the quasi-stationary measure $μ$-almost surely. We apply this result to the random logistic map $X_{n+1} = ω_n X_n (1-X_n)$ absorbed at $\mathbb R \setminus [0,1],$ where $ω_n$ is an i.i.d sequence of random variables uniformly distributed in $[a,b],$ for $1\leq a <4$ and $b>4.$
