论文标题
离散时间马尔可夫链的摄动理论和统一的磨牙性
Perturbation theory and uniform ergodicity for discrete-time Markov chains
论文作者
论文摘要
我们根据某些集合第一次打击时间的均匀力矩来研究一般状态空间上离散时间马尔可夫链的扰动理论和统一的登山性。我们采用的方法与以前的方法不同。对于可逆和非负明确的马尔可夫链，我们首先研究了几何偏僻的收敛速率。基于估计值，以及第一个通过公式，我们将收敛速率均匀地延伸。如果过渡内核$ p $仅是可逆的，我们将转移到使用过渡内核$ p^2 $的两型骨骼链。在技术层面上，关键点是将第一个返回时间的几何时刻连接在$ p $和$ p^2 $之间。
We study perturbation theory and uniform ergodicity for discrete-time Markov chains on general state spaces in terms of the uniform moments of the first hitting times on some set. The methods we adopt are different from previous ones. For reversible and non-negative definite Markov chains, we first investigate the geometrically ergodic convergence rates. Based on the estimates, together with a first passage formula, we then get the convergence rates in uniform ergodicity. If the transition kernel $P$ is only reversible, we transfer to study the two-skeleton chain with the transition kernel $P^2$. At a technical level, the crucial point is to connect the geometric moments of the first return times between $P$ and $P^2$.
