We continue the work of improving the rate of convergence of ergodic homogeneous Markov chains. The setting is more general than in previous papers: we are able to get rid of the assumption about a common dominating measure and consider the case of inhomogeneous Markov chains as well as more general state spaces. We give examples where the new bound for the rate of convergence is the same as (resp. better than) the classical Markov–Dobrushin inequality.

中文翻译：

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关于马尔可夫链收敛的改进界限和条件

我们继续致力于提高遍历齐次马尔可夫链的收敛速度。该设置比以前的论文更通用：我们能够摆脱关于共同主导测度的假设，并考虑非齐次马尔可夫链以及更通用的状态空间的情况。我们给出的例子中，收敛速度的新界限与经典的马尔可夫-多布鲁辛不等式相同（或者更好）。