On the existence of recurrent extensions of self-similar Markov processes. (English) Zbl 1110.60036

Summary: Let \(X=(X_t)_{t\leq 0}\) be a self-similar Markov process with values in the nonnegative half-line, such that the state 0 is a trap. We present a necessary and sufficient condition for the existence of a self-similar recurrent extension of \(X\) that leaves 0 continuously. This condition is expressed in terms of the Lévy process associated with \(X\) by the Lamperti transformation.


60G18 Self-similar stochastic processes
60G51 Processes with independent increments; Lévy processes
60J45 Probabilistic potential theory
60J55 Local time and additive functionals
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