Markov processes with identical last exit distributions

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.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