A note on capacitary measures of semipolar sets
The author considers a pair of standard processes with stochastic resolvents in strong duality, and he shows that for a Borel set S in the state space satisfying \(S\subset \{P_ S1<\epsilon\), \(\hat P_ S1<\epsilon \}\) for some \(\epsilon\in (0,1]\) (where \(P_ S\), \(\hat P_ S\) denote the respective hitting kernels) there exists a \(\sigma\)-finite measure \(\pi\) on S satisfying the following condition: A Borel subset B of S is polar if and only if \(\pi (B)=0.\) According to a more general result by \textit{C. Dellacherie}, \textit{D. Feyel} and \textit{G.Mokobodzki} [Séminaire de probabilités XVI, Univ. Strasbourg 1980/81, Lect. Notes Math. 920, 8-28 (1982; Zbl 0496.60076)] this property characterizes S to be semipolar. The author shows, moreover, that the measure \(\pi\) may be chosen as the capacitary measure with respect to a \(\lambda\)-subprocess \((\lambda >0)\) provided \(\epsilon <1.\) In a recent preprint ``Remarks on a paper of Kanda'', \textit{P. J. Fitzsimmons} has strengthened the author's result and simplified its proof.
scientific article; zbMATH DE number 4096526