This paper provides sufficient conditions over the sequence of samples and parameters of an adaptive Markov Chain Monte Carlo (MCMC) algorithm to ensure ergodicity with respect to a target distribution that can have unbounded support. These conditions aim to make more easily usable the conditions of Containment and Diminishing Adaptation from Roberts and Rosenthal [2007] formulated over the transition kernels, without needing, as was done in other works, an artificial assumption of the compactness over both sample and parameter spaces. The paper shows that the condition of compactness can be relaxed to a more realistic bound in probability over the sequence of both samples and parameters.

翻译：本文针对自适应马尔可夫链蒙特卡洛（MCMC）算法的样本序列与参数序列，提出了确保其关于具有无界支撑的目标分布具有遍历性的充分条件。这些条件旨在使Roberts与Rosenthal [2007] 针对转移核所提出的"包容性"与"适应衰减"条件更易于应用，而无需如其他研究那样对样本空间与参数空间施加人为的紧致性假设。本文证明，紧致性条件可以放宽为对样本序列与参数序列施加更符合实际应用的概率有界约束。