Summary
If X t is a Hunt process and T = inf{t>0: (X t−,Xt)∃KxL,X t− ≠ Xt}, the distribution of X(T) can be determined from a cone of functions calculable from the potential of X and the Lévy system of X. The method involves studying the time change Y t of X t by the inverse of a discontinuous additive functional. We complete Weidenfeld's study of time changing X t by the inverse of C t by showing that Y t (restricted to its nonbranch points) is a right process if X t is a “right semiregenerative process” on \(M \cup \prod = \hat {\rm M}\) where:
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(1)
¯M is the closed support of C t, M is the minimal right closed set with closure ¯M, and π=⋆:C t-C t}->0.
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(2)
¯M is homogeneous.
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(3)
C t is additive on \(\hat M \cup [0]\)
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Research supported by an NSF Postdoctoral Research Fellowship in the Mathematical Sciences while visiting University of California, San Diego.
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Glover, J. Discontinuous time changes of semiregenerative processes and balayage theorems. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 145–160 (1983). https://doi.org/10.1007/BF00535001
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DOI: https://doi.org/10.1007/BF00535001