Abstract
Let (X(t),P x) and (X(t))},PP}x) be two Hunt processes in duality with respect to an excessive measure ξ and having resolvents that commute. The main result of this article is that if there is an ε with 0<ε<1 so that (U 1 U 1 f,f)⩾−ε‖U 1 f‖2 for everyf in ℒ2(ξ), thenX(t) satisfies Hunt's hypothesis (H): every set that is semipolar forX(t) is polar forX(t).
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Glover, J., Rao, M. Nonsymmetric Markov processes and hypothesis (H). J Theor Probab 1, 371–380 (1988). https://doi.org/10.1007/BF01048726
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DOI: https://doi.org/10.1007/BF01048726