The spase of exits of a Markov process

Martin's theory makes it possible to describe the sets of all non-negative harmonic and superharmonic functions in an arbitrary domain of euclidean space. To each Markov process there corresponds the class of so-called excessive functions, analogous in their properties to the class of non-negative superharmonic functions. The study of this class is closely connected with the study of “the space of exits of a Markov process”. Corresponding results for discrete Markov chains were obtained by Doob, Hunt and Watanabe, and for certain types of processes with variable time by Kunita and Watanabe. The paper gives an account of the general theory, which includes as particular cases all the results listed.