Summary
LetX andY be two transient locally Hunt Markov processes. IfX andY enjoy the same last exit distributions from compact sets, thenY is equivalent to a time change ofX by the inverse of a strictly increasing continuous additive functional. This result can also be interpreted (with natural auxiliary hypotheses) as a statement in potential theory involving equilibrium measures.
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Research supported in part by NSF grant MCS-8002659 and an CNRS Fellowship while the author was visiting I.M.S.S., Universite de Grenoble II
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Glover, J. Markov processes with identical last exit distributions. Z. Wahrscheinlichkeitstheorie verw Gebiete 59, 67–75 (1982). https://doi.org/10.1007/BF00575526
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DOI: https://doi.org/10.1007/BF00575526