On the asymptotic behaviour of increasing self-similar Markov processes ∗

  title={On the asymptotic behaviour of increasing self-similar Markov processes ∗},
  author={Maria Emilia Caballero},
It has been proved by Bertoin and Caballero [8] that a 1/α-increasing self-similar Markov process X is such that tX (t) converges weakly, as t →∞, to a degenerate random variable whenever the subordinator associated to it via Lamperti’s transformation has infinite mean. Here we prove that log(X (t)/t)/ log(t) converges in law to a non-degenerate random variable if and only if the associated subordinator has Laplace exponent that varies regularly at 0. Moreover, we show that lim inft→∞ log(X (t… CONTINUE READING

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