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Markov properties of multiparameter processes and capacities
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  • Published: March 1995

Markov properties of multiparameter processes and capacities

  • F. Hirsch1 &
  • S. Song1 

Probability Theory and Related Fields volume 103, pages 45–71 (1995)Cite this article

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Summary

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.

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Authors and Affiliations

  1. Equipe d'Analyse et probabilités, Université d'Evry-Val d'Essonne, Boulevard des Coquibus, F-91025, eVRY Cedex, France

    F. Hirsch & S. Song

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  1. F. Hirsch
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  2. S. Song
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Hirsch, F., Song, S. Markov properties of multiparameter processes and capacities. Probab. Th. Rel. Fields 103, 45–71 (1995). https://doi.org/10.1007/BF01199031

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  • Received: 22 July 1994

  • Revised: 03 April 1995

  • Issue Date: March 1995

  • DOI: https://doi.org/10.1007/BF01199031

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Mathematics subject classification

  • 31C15
  • 60J25
  • 60J30
  • 60J45
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