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

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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

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Probability, 60F99, 60G18, 60G52, 60J55

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http://salesiana.dossiersoluciones.com/handle/123456789/138047

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701653
 http://arxiv.org/abs/math/0701653

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arXiv