Recurrent Extensions
of Self-similar Markov Processes
On the Existence of Recurrent Extensions
of Self-similar Markov Processes
P.J. Fitzsimmons
Let X=(Xt) 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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(Version of March 28, 2006)
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March 28, 2006
