The basic aim of this paper is to provide a fundamental tool, the resolvent decomposition theorem, in the construction theory of denumerable Markov processes. We present a detailed analytic proof of this extremely useful tool and explain its clear probabilistic interpretation. We then apply this tool to investigate the basic problems of existence and uniqueness criteria for denumerable Markov processes with instantaneous states to which few results have been obtained even until now. Although the complete answers regarding these existence and uniqueness criteria will be given in a subsequent paper, we shall, in this paper, present part solutions of these very important problems that are closely linked with the subtle Williams S and N conditions.

中文翻译：

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可解分解定理及其在瞬态可数马尔可夫过程中的应用

本文的基本目的是在可数马尔可夫过程的构造理论中提供一个基本工具，即解析分解定理。我们提供了这个极其有用的工具的详细分析证明，并解释了其清晰的概率解释。然后，我们应用此工具来研究具有瞬时状态的可数马尔可夫过程的存在性和唯一性标准的基本问题，即使到现在为止也很少获得结果。虽然关于这些存在唯一性标准的完整答案将在后续论文中给出，但我们将在本文中提出这些与微妙的威廉姆斯 S 和 N 条件密切相关的非常重要问题的部分解决方案。