Small deviations of general Lévy processes
نویسنده
چکیده
We study the small deviation problem logP(supt∈[0,1] |Xt| 6 ε), as ε → 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 non-vanishing Gaussian component has the same (strong) asymptotic small deviation rate as the corresponding Brownian motion.
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