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

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

2007-01-23

arxiv.org/abs/math/0701653v2

Mathematics

Probability

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

Scientific paper

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.

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