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

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.

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

References in corpus (2)

• Persistence of a Rouse polymer chain under transverse shear flow
• On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial data

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