We investigate the concatenation of Markov processes. Our primary concern is to utilize processes constructed in this manner for Monte Carlo integration. To enable this using conventional methods, it is essential to demonstrate the Markov property and invariance with respect to a given target distribution. We provide mild sufficient conditions for this. Our main result is the identification of the generator of the concatenation of Markov processes. This result provides the theoretical foundation for Monte Carlo methods based on this construction.

翻译：本文研究马尔可夫过程的串联构造。我们主要关注如何利用此类过程实现蒙特卡洛积分。为通过传统方法实现该目标，必须证明其满足马尔夫性且对给定目标分布具有不变性。我们为此提出了温和的充分条件。主要成果在于识别了串联马尔可夫过程的生成元，该结果为基于此构造的蒙特卡洛方法奠定了理论基础。