Hunt’s hypothesis (H) and Getoor’s conjecture. (English) Zbl 0602.60063

For a standard process X, the Hunt hypothesis (H) is stated as follows: Every semipolar Borel set is polar. If X is symmetric relative to some \(\sigma\)-finite measure, then X satisfies (H). In the cases of Lévy processes and processes associated with non-symmetric Dirichlet spaces, some sufficient conditions for (H) are known.
In this paper, the authors show that, for a standard process X and an independent subordinator T satisfying (H), the subordinated process \(X(T_ t)\) satisfies (H). In particular, by taking T as the stable process of index \(0<\alpha <1\), the Lévy process \(X^{\alpha}\) with exponent \(\Phi^{\alpha}\) satisfies (H).
Reviewer: Y.Ōshima


60J45 Probabilistic potential theory
31D05 Axiomatic potential theory
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