Contributions to the Theory of Markov Chains

The fundamentals of the theory of denumerable Markov chains with stationary transition probabilities were laid down by Kolmogorov, and further work was done by Doblin. The theory of recurrent events of Feller is closely related, if not coextensive. Some new results obtained by T. E. Harris turn out to tie up very nicely with some amplifications of Doblin's work. Harris was led to consider the probabilities of hitting one state before another, starting from a third one. This idea of considering three states, one initial, one “taboo”, and one final, is more fully developed in the present work. The notion of first passage time to the “union” or “intersection” of two states is also introduced here. The interplay between these notions is illustrated.