Small deviations of general L\'evy processes
Abstract
We study the small deviation problem (t∈[0,1]|Xt|≤), as 0, for general L\'evy processes X. The techniques enable us to determine the asymptotic rate for general real-valued L\'evy processes, which we demonstrate with many examples. As a particular consequence, we show that a L\'evy process with nonvanishing Gaussian component has the same (strong) asymptotic small deviation rate as the corresponding Brownian motion.
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