Conditioned Stable Lévy Processes and the Lamperti Representation

  title={Conditioned Stable L{\'e}vy Processes and the Lamperti Representation},
  author={Maria Emilia Caballero},
By variously killing a stable Lévy process when it leaves the positive half-line, conditioning it to stay positive, and conditioning it to hit 0 continuously, we obtain three different, positive, self-similar Markov processes which illustrate the three classes described by Lamperti (1972). For each of these processes, we explicitly compute the infinitesimal generator and from this deduce the characteristics of the underlying Lévy process in the Lamperti representation. The proof of this result… CONTINUE READING
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