Probability on the Existence of Recurrent Extensions of Self-similar Markov Processes

  title={Probability on the Existence of Recurrent Extensions of Self-similar Markov Processes},
  author={Patrick J. Fitzsimmons},
Let X = (Xt)t≥0 be a self-similar Markov process with values in [0,∞[, 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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