CONTINUOUS PARAMETER MARKOV CHAINS
This paper was prepared with the partial support of the Office of Scientific Research of the United States Air Force.
The name given in the title is an abbreviation of ‘Markov processes with continuous time parameter, denumerable state space and stationary transition probabilities’. This theory is to the discrete parameter theory as functions of a real variable are to infinite sequences. New concepts and problems arise which have no counterpart in the latter theory. Owing to the sharply denned nature of the process, these problems are capable of precise and definitive solutions, and the methodology used well illustrates the general notions of stochastic processes. It is possible that the results obtained in this case will serve as a guide in the study of more general processes. The theory has contacts with that of martingales and of semi-groups which have been encouraging and may become flourishing. For lack of space the developments from the standpoint of semi-groups or systems of differential equations cannot be discussed here…
