Recurrent Extensions
of Self-similar Markov Processes
### On the Existence of Recurrent Extensions
of Self-similar Markov Processes

#### P.J. Fitzsimmons

Let *X=(X*_{t}) be a self-similar Markov process with values in
the non-negative 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.

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March 28, 2006