The asymptotic of products of general Markov/transition kernels is investigated using Doeblin’s coefficient. We propose a general approximating scheme as well as a convergence rate in total variation of such products by a sequence of positive measures. These approximating measures and the control of convergence are explicit from the two parameters in the minorization condition associated with the Doeblin coefficient. This allows us to extend the well-known forward/backward convergence results for stochastic matrices to general Markov kernels. A new result for forward/backward products of random Markov kernels is also established.

中文翻译：

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马尔可夫核积的渐近线。应用于确定性和随机正向/反向产品

使用 Doeblin 系数研究了一般马尔可夫/转移核的乘积的渐近性。我们通过一系列积极的措施提出了一个通用的近似方案以及这些产品总变化的收敛率。从与 Doeblin 系数相关的小化条件中的两个参数来看，这些近似测量和收敛控制是明确的。这允许我们将众所周知的随机矩阵的前向/后向收敛结果扩展到一般马尔可夫核。还建立了随机马尔可夫核的前向/后向乘积的新结果。