English

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

R2 v1 2026-06-21T19:19:14.805Z