Summary
Let X tbe a transient Hunt process having a potential density u(x) chosen in the usual way. No duality hypotheses are assumed. Let K be a closed set with M=sup{t:X t∈K}<∞ almost surely. For f a bounded Borel function,
, where κ is a measure on E, and ν cis a measure on E×E so that ν c(E−K) ×E)=0. If X t is simply a right process and K is closed,
. If X tis a right process and K ⊂E is closed in the Ray topology of X, then
. If X tis a diffusion, we obtain the representation of equilibrium potentials (for closed sets) due to Chung, Getoor-Sharpe, and Meyer without duality hypotheses.
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Research supported in part by NSF grant MCS-8002659 and a CNRS Fellowship while the author was visiting I.M.S.S., Universite de Grenoble II
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Glover, J. Representing last exit potentials as potentials of measures. Z. Wahrscheinlichkeitstheorie verw Gebiete 61, 17–30 (1982). https://doi.org/10.1007/BF00537222
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DOI: https://doi.org/10.1007/BF00537222