The lower tail problem for homogeneous functionals of stable processes with no negative jumps

Thomas Simon

The lower tail problem for homogeneous functionals of stable processes with no negative jumps

Probability 2007-09-17 v2

Authors: Thomas Simon

Abstract

Let Z be a strictly a-stable real Levy process (a>1) and X be a fluctuating b-homogeneous additive functional of Z. We investigate the asymptotics of the first passage-time of X above 1, and give a general upper bound. When Z has no negative jumps, we prove that this bound is optimal and does not depend on the homogeneity parameter b. This extends a result of Y. Isozaki and solves partially a conjecture of Z. Shi.

Keywords

lévy processes

Cite

@article{arxiv.math/0701653,
  title  = {The lower tail problem for homogeneous functionals of stable processes with no negative jumps},
  author = {Thomas Simon},
  journal= {arXiv preprint arXiv:math/0701653},
  year   = {2007}
}

Comments

Revised version. To appear in ALEA Latin American Journal of Probability and Mathematical Statistics

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