Central and Non-central Limit Theorems in a Free Probability Setting

Ivan Nourdin () and Murad S. Taqqu ()
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Ivan Nourdin: Institut de Mathématiques Élie Cartan, Université de Lorraine
Murad S. Taqqu: Boston University

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 220-248

Abstract: 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: Central limit theorem; Non-central limit theorem; Convergence in distribution; Fractional Brownian motion; Free Brownian motion; Free probability; Rosenblatt process; Wigner integral; 46L54; 60H05; 60H07 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0443-2

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