Sato, Sadao On the reconstruction of a killed Markov process. (English) Zbl 0772.60052 Séminaire de probabilités XXVI, Lect. Notes Math. 1526, 540-559 (1992). [For the entire collection see Zbl 0754.00008.]Let \((X_ t)\) be a killed Markov process. We mainly discuss a method to reconstruct a (conservative) process \((Y_ t)\) to which \((X_ t)\) is subordinated. This problem was discussed by N. Ikeda, M. Nagasawa and S. Watanabe [Proc. Japan Acad. 42, 370-375 (1966; Zbl 0178.534)], and an excellent result was obtained by K. Itô and S. Watanabe [Colloques Int. Centre nat. Rech. sci. 146, 13-30 (1965; Zbl 0141.151)]. We study the conservativity of a related multiplicative functional, which was already obtained by Itô and Watanabe by constructing conservative \((Y_ t)\). We give it another proof by an analytic method which is more simple and direct. We also give a basic inversion formula of killing. Reviewer: S.Sato (Tokyo) Cited in 1 Document MSC: 60J25 Continuous-time Markov processes on general state spaces Keywords:killed Markov process; multiplicative functional; inversion formula of killing Citations:Zbl 0754.00008; Zbl 0178.534; Zbl 0141.151 PDFBibTeX XMLCite \textit{S. Sato}, Lect. Notes Math. 1526, 540--559 (1992; Zbl 0772.60052) Full Text: Numdam EuDML