Probability Theory and Related Fields

, Volume 103, Issue 1, pp 45–71

Markov properties of multiparameter processes and capacities

  • F. Hirsch
  • S. Song

DOI: 10.1007/BF01199031

Cite this article as:
Hirsch, F. & Song, S. Probab. Th. Rel. Fields (1995) 103: 45. doi:10.1007/BF01199031


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.

Mathematics subject classification

31C15 60J25 60J30 60J45 

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • F. Hirsch
    • 1
  • S. Song
    • 1
  1. 1.Equipe d'Analyse et probabilitésUniversité d'Evry-Val d'EssonneeVRY CedexFrance