Exact Edgeworth expansion for a L\'evy process
Abstract
The one dimensional distribution of a L\'evy process is not known in general even though its characteristic function is given by the famous L\'evy-Khinchine theorem. This article gives an exact series representation for the one dimensional distribution of a L\'evy process satisfying certain moment conditions. Moreover, this work clarifies an old result by Cram\'er on Edgeworth expansions for the distribution function of a L\'evy process.
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