Cramer's estimate for a reflected Levy process

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dc.creatorDoney, R. A.
dc.creatorMaller, R. A.
dc.date2005-05-12
dc.date.accessioned2026-07-07T05:19:50Z
dc.date.available2026-07-07T05:19:50Z
dc.descriptionThe natural analogue for a Levy process of Cramer's estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measure of the height of an excursion above the minimum. We establish this estimate for any Levy process with finite negative mean which satisfies Cramer's condition, and give an explicit formula for the limiting constant. Just as in the random walk case, this leads to a Poisson limit theorem for the number of ``high excursions.''
dc.descriptionPublished at http://dx.doi.org/10.1214/105051605000000016 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0505246
dc.identifierhttp://arxiv.org/abs/math/0505246
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 2, 1445-1450
dc.identifierdoi:10.1214/105051605000000016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75166
dc.subjectProbability
dc.subject60G51, 60G17. (Primary)
dc.titleCramer's estimate for a reflected Levy process
dc.typetext

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