Markov properties of multiparameter processes and capacities
- Cite this article as:
- Hirsch, F. & Song, S. Probab. Th. Rel. Fields (1995) 103: 45. doi:10.1007/BF01199031
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We study a class of multiparameter symmetric Markov processes. We prove that this class is stable by subordination in Bochner's sense. We show then that for these processes, a probabilistic and an analytic potential theory correspond to each other. In particular, additive functionals are associated with finite energy measures, hitting probabilities are estimated by capacities, quasicontinuity corresponds to path-continuity. In the last section, examples show that many earlier results, as well as new ones, in this domain can be obtained by our method.