Geodesic
Excessive functions and the exit-space of a~Markov process
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 38-55

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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. 
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     author = {E. B. Dynkin},
     title = {Excessive functions and the exit-space of {a~Markov} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {38--55},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a2/}
}
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E. B. Dynkin. Excessive functions and the exit-space of a~Markov process. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 38-55. http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a2/