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

Thomas Simon

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

Thomas Simon

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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.

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Thomas Simon. 2007-09-17. The lower tail problem for homogeneous functionals of stable processes with no negative jumps. https://arxiv.org/abs/math/0701653

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