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Construction of Markov processes and associated multiplicative functionals from given harmonic measures
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  • Published: June 1994

Construction of Markov processes and associated multiplicative functionals from given harmonic measures

  • C. T. Shih1 

Probability Theory and Related Fields volume 98, pages 185–207 (1994)Cite this article

Summary

LetE be a noncompact locally compact second countable Hausdorff space. We consider the question when, given a family of finite nonzero measures onE that behave like harmonic measures associated with all relatively compact open sets inE (i.e. that satisfy a certain consistency condition), one can construct a Markov process onE and a multiplicative functional with values in [0, ∞) such that the hitting distributions of the process “inflated” by the multiplicative functional yield the given harmonic measures. We achieve this construction under weak continuity and local transience conditions on these measures that are natural in the theory of Markov processes, and a mild growth restriction on them. In particular, if the spaceE equipped with the measures satisfies the conditions of a harmonic space, such a Markov process and associated multiplicative functional exist. The result extends in a new direction the work of many authors, in probability and in axiomatic potential theory, on constructing Markov processes from given hitting distributions (i.e. from harmonic measures that have total mass no more than 1).

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Authors and Affiliations

  1. Mathematics Department, University of Michigan, 48109, Ann Arbor, MI, USA

    C. T. Shih

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  1. C. T. Shih
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Shih, C.T. Construction of Markov processes and associated multiplicative functionals from given harmonic measures. Probab. Th. Rel. Fields 98, 185–207 (1994). https://doi.org/10.1007/BF01192513

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  • Received: 12 December 1992

  • Revised: 21 September 1993

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01192513

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Mathematics Subject Classification (1991)

  • 60J40
  • 60J45
  • 31D05
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