Universality of the asymptotics of the one-sided exit problem for integrated processes

@article{Aurzada2010UniversalityOT,
  title={Universality of the asymptotics of the one-sided exit problem for integrated processes},
  author={F. Aurzada and S. Dereich},
  journal={arXiv: Probability},
  year={2010}
}
We consider the one-sided exit problem for (fractionally) integrated random walks and L\'evy processes. We prove that the rate of decrease of the non-exit probability -- the so-called survival exponent -- is universal in this class of processes. In particular, the survival exponent can be inferred from the (fractionally) integrated Brownian motion. This, in particular, extends Sinai's result on the survival exponent for the integrated simple random walk to general random walks with some finite… Expand
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