Asymptotic properties of power variations of L\'{e}vy processes
Probability
2007-05-23 v1
Abstract
We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior (convergence in probability, possibly after normalization). As for the associated CLT, one can show some versions of it, but only in a limited number of cases. In some other cases, a CLT just does not exist.
Cite
@article{arxiv.math/0511052,
title = {Asymptotic properties of power variations of L\'{e}vy processes},
author = {Jean Jacod},
journal= {arXiv preprint arXiv:math/0511052},
year = {2007}
}