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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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