Central and non-central limit theorems in a free probability setting
Probability
2012-05-31 v4 Operator Algebras
Abstract
Long-range dependence in time series may yield non-central limit theorems. We show that there are analogous time series in free probability with limits represented by multiple Wigner integrals, where Hermite processes are replaced by non-commutative Tchebycheff processes. This includes the non-commutative fractional Brownian motion and the non-commutative Rosenblatt process.
Keywords
Cite
@article{arxiv.1110.2703,
title = {Central and non-central limit theorems in a free probability setting},
author = {Ivan Nourdin and Murad Taqqu},
journal= {arXiv preprint arXiv:1110.2703},
year = {2012}
}
Comments
26 pages