Exact Edgeworth expansion for a Lévy process

Details Exact Edgeworth expansion for a Lévy process Exact Edgeworth expansion for a Lévy process

2008-05-28

arxiv.org/abs/0805.4332v2

Mathematics

Probability

Scientific paper

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

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