Central and non-central limit theorems in a free probability setting
Taqqu, Murad S.
MetadataShow full item record
Citation (published version)Ivan Nourdin, Murad S Taqqu. 2014. "Central and Non-central Limit Theorems in a Free Probability Setting." JOURNAL OF THEORETICAL PROBABILITY, Volume 27, Issue 1, pp. 220 - 248 (29). https://doi.org/10.1007/s10959-012-0443-2
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.