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arXiv · 1110.2703

Central and non-central limit theorems in a free probability setting

Ivan Nourdin·Murad Taqqu
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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.

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Ivan Nourdin, Murad Taqqu. 2012-05-30. Central and non-central limit theorems in a free probability setting. https://arxiv.org/abs/1110.2703

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