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Zbl 0772.60052
Sato, Sadao
On the reconstruction of a killed Markov process. (English)
[A] Séminaire de probabilités XXVI, Lect. Notes Math. 1526, 540-559 (1992). ISBN 3-540-56021-1/pbk

[For the entire collection see Zbl 0754.00008.]\par Let $(X\sb t)$ be a killed Markov process. We mainly discuss a method to reconstruct a (conservative) process $(Y\sb t)$ to which $(X\sb t)$ is subordinated. This problem was discussed by {\it N. Ikeda}, {\it M. Nagasawa} and {\it S. Watanabe} [Proc. Japan Acad. 42, 370-375 (1966; Zbl 0178.534)], and an excellent result was obtained by {\it K. Itô} and {\it 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 $(Y\sb t)$. We give it another proof by an analytic method which is more simple and direct. We also give a basic inversion formula of killing.
[S.Sato (Tokyo)]

MSC 2000:: *60J25 Markov processes with continuous parameter

Keywords: killed Markov process; multiplicative functional; inversion formula of killing

Citations: Zbl 0754.00008; Zbl 0178.534; Zbl 0141.151

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