Exact Edgeworth expansion for a L\'{e}vy process
Probability
2008-09-15 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0805.4332,
title = {Exact Edgeworth expansion for a L\'{e}vy process},
author = {Heikki J. Tikanmäki},
journal= {arXiv preprint arXiv:0805.4332},
year = {2008}
}