This article is cited in 3 papers

Excessive functions and the exit-space of a Markov process

E. B. Dynkin

Moscow

Abstract: The Martin theory enables to describe the set of all positive superharmonic functions in a domain of an Euclidean space. A class of excessive functions (the natural generalization of positive superharmonic functions) corresponds to any Markov process. There exist close relations between the excessive functions and the so-called exit-space of a Markov process. These topics were investigated by Doob, Hunt, Watanabe (for discrete Markov chains) and by Kunita and Watanabe (for some types of continuous-time processes). We develop a general theory which contains as special cases the results of the authors above.

Received: 24.03.1969

 English version: Theory of Probability and its Applications, 1970, 15:1, 37–54

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