Small deviations of general Lévy processes
Aurzada, Frank ; Dereich, Steffen
Ann. Probab., Tome 37 (2009) no. 1, p. 2066-2092 / Harvested from Project Euclid
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We study the small deviation problem logℙ(sup t∈[0, 1]|Xt|≤ɛ), as ɛ→0, for general Lévy processes X. The techniques enable us to determine the asymptotic rate for general real-valued Lévy processes, which we demonstrate with many examples. ¶ As a particular consequence, we show that a Lévy process with nonvanishing Gaussian component has the same (strong) asymptotic small deviation rate as the corresponding Brownian motion.
Publié le : 2009-09-15
Classification:  Small deviations,  small ball problem,  lower tail probability,  Lévy process,  Esscher transform,  60G51 
@article{1253539864,
     author = {Aurzada, Frank and Dereich, Steffen},
     title = {Small deviations of general L\'evy processes},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 2066-2092},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1253539864}
}

Aurzada, Frank; Dereich, Steffen. Small deviations of general Lévy processes. Ann. Probab., Tome 37 (2009) no. 1, pp.  2066-2092. http://gdmltest.u-ga.fr/item/1253539864/