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

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

2011-10-12

arxiv.org/abs/1110.2703v2

Mathematics

Probability

24 pages

Scientific paper

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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