Duality Under a New Setting

  • K. L. Chung
  • Ming Liao
  • K. M. Rao
Part of the Progress in Probability and Statistics book series (PRPR, volume 7)


This is a continuation of [2]. The developments there are complicated by an exceptional set denoted by Z (see [2], p. 179). It is shown that Z is a polar set under the conditions there if and only if Hunt’s Hypothesis (B) holds (see [2], p, 192). In this paper a set of sufficcient conditions on the potential kernel will be given for the absence of Z. These strengthen the conditions used in [2]. The dual semigroup {P0302t, t ≥ 0} (see 2 , p. 191) is then defined on the state space E, some of its properties will be reviewed and adduced. A process will then be constructed with the dual semigroup as its transition semigroup, which will be shown to be a Hunt process on E. This process is in (strong) duality with the original Hunt Process in the sense of [1].


Radon Measure Markov Property Dual Process Excessive Function Strong Markov Property 
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Copyright information

© Birkhäuser Boston, Inc. 1984

Authors and Affiliations

  • K. L. Chung
    • 1
  • Ming Liao
    • 1
  • K. M. Rao
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA

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