This paper provides sufficient conditions over the sequence of samples and parameters of an adaptive Markov Chain Monte Carlo (MCMC) algorithm to converge to the target distribution. These conditions aim to make more easily usable classical conditions formulated over the transition kernels, without needing, as was done in other works, to assume the compactness of both sample and parameter spaces. The condition of compactness is replaced here with a probability bound 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，给出了保证其样本序列与参数序列收敛至目标分布的充分条件。这些条件旨在使传统基于转移核表述的条件更易于应用，无需如现有研究那样假设样本空间与参数空间的紧致性。本文通过引入对样本序列与参数序列的概率界约束，替代了原有的紧致性条件。