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A class of path-valued Markov processes and its applications to superprocesses
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  • Published: March 1993

A class of path-valued Markov processes and its applications to superprocesses

  • J. F. Le Gall1 

Probability Theory and Related Fields volume 95, pages 25–46 (1993)Cite this article

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Summary

Let (ξ s ) be a continuous Markov process satisfying certain regularity assumptions. We introduce a path-valued strong Markov process associated with (ξ s ), which is closely related to the so-called superprocess with spatial motion (ξ s ). In particular, a subsetH of the state space of (ξ s ) intersects the range of the superprocess if and only if the set of paths that hitH is not polar for the path-valued process. The latter property can be investigated using the tools of the potential theory of symmetric Markov processes: A set is not polar if and only if it supports a measure of finite energy. The same approach can be applied to study sets that are polar for the graph of the superprocess. In the special case when (ξ s ) is a diffusion process, we recover certain results recently obtained by Dynkin.

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Authors and Affiliations

  1. Laboratoire de Probabilités, Université Paris VI, 4 Place Jussieu, Tour 56 3ème Etage, F-75252, Paris Cedex 05, France

    J. F. Le Gall

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  1. J. F. Le Gall
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Le Gall, J.F. A class of path-valued Markov processes and its applications to superprocesses. Probab. Th. Rel. Fields 95, 25–46 (1993). https://doi.org/10.1007/BF01197336

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  • Received: 12 August 1991

  • Revised: 01 June 1992

  • Issue Date: March 1993

  • DOI: https://doi.org/10.1007/BF01197336

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Mathematics Subject Classification

  • 60 J 25
  • 60 J 45
  • 60 G 57
  • 60 J 60
  • 60 J 80
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