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Time-changes of self-similar Markov processes. (English) Zbl 0698.60062
Summary: Let $$X_ t$$ be a $$\beta$$-self-similar, $$\beta >0$$, transient Markov process on (0,$$\infty)$$. We show that if $$X_{T_ t}$$ $$(T_ t$$ is the right continuous inverse of a continuous additive functional $$A_ t)$$ is an $$\alpha$$-self-similar Markov process, $$\alpha >0$$, then $A_ t=k\int^{t}_{0}X_ h^{1/\alpha -1/\beta}dh\quad for\quad some\quad k>0.$ A result concerning time-changes of a transient Lévy process is also given.

##### MSC:
 60J25 Continuous-time Markov processes on general state spaces
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