Fitzsimmons, P. J.; Getoor, R. K.; Sharpe, M. J. The Blumenthal-Getoor-McKean theorem revisited. (English) Zbl 0744.60090 Stochastic processes, Semin., San Diego/CA (USA) 1989, Prog. Probab. 18, 35-57 (1990). From the introduction: The Blumenthal-Getoor-McKean theorem [see R. M. Blumenthal, R. K. Getoor and H. P. McKean jun., Ill. J. Math. 6, 402–420 (1962; Zbl 0133.40903) and ibid. 7, 540–542 (1963; Zbl 0211.48602), hereafter referred to as BGM] states that if \(X\) and \(\tilde X\) are two Markov processes with the same hitting distributions, then they may be time changed into each other. This is a deliberately loose statement and one needs to specify the precise hypotheses on \(X\) and \(\tilde X\) and also exactly what the conclusion means before it makes mathematical sense. In §V-5 of [R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory. New York etc.: Academic Press (1968; Zbl 0169.49204)], hereafter referred to as BG, a precise statement and proof are given when \(X\) and \(\tilde X\) are standard processes as defined in [BG]. It is stated in several places in the literature that the proof in [BG] carries over to the case in which \(X\) and \(\tilde X\) are right processes. However, a careful reading of that proof reveals that the quasi-left-continuity (qlc) of \(X\) and \(\tilde X\) is used in a crucial manner at two points: the proofs of (V-5.4) and (V-5.20) in [BG]. The purpose of this paper is to give a careful proof of BGM for arbitrary right processes \(X\) and \(\tilde X\) as defined in [M. J. Sharpe, General theory of Markov processes. Boston, MA: Academic Press (1988; Zbl 0649.60079)].[For the entire collection see Zbl 0686.00017.] Cited in 3 Documents MSC: 60J45 Probabilistic potential theory Keywords:Blumenthal-Getoor-McKean theorem; standard processes; right processes Citations:Zbl 0686.00017; Zbl 0133.40903; Zbl 0211.48602; Zbl 0169.49204; Zbl 0649.60079 PDFBibTeX XMLCite \textit{P. J. Fitzsimmons} et al., Prog. Probab. None, 35--57 (1990; Zbl 0744.60090)