×

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)

MSC:

60J25 Continuous-time Markov processes on general state spaces
PDFBibTeX XMLCite
Full Text: Numdam EuDML