ON THE MARTIN BOUNDARY FOR MARKOV CHAINS

The Martin boundary for a discrete parameter Markov chain was first considered by Doob,² using the theory of R. S. Martin after whom the boundary is named. A direct and ingenious method was later found by Hunt,³ who also strengthened Doob's results in several points. In this note, I shall sketch a natural approach to the theory in the continuous parameter case. There, upon the introduction of certain intrinsic quantities (probabilities) which have no obvious discrete analogues, it is possible to derive the main results by familiar methods developed in reference…