Compactification of the discrete state space of a Markov process

Summary The countable state space of a Markov chain whose stationary transition probabilities satisfy the continuity condition (1.5) is compactifled to get a state space on which the corresponding processes can be made right continuous with left limits, and strongly Markovian. There is a form of quasi left continuity, modified by the possible presence of branch points. Excessive functions are investigated.