Abstract
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.
Citation
Frank Aurzada. Steffen Dereich. "Small deviations of general Lévy processes." Ann. Probab. 37 (5) 2066 - 2092, September 2009. https://doi.org/10.1214/09-AOP457
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