Abstract
In the previous chapter, we showed that normalized sums associated to a stationary sequence with long-range dependence may yield a non-central limit theorem (Theorem 7.3). Here, motivated by the fact that there is often a close correspondence between classical probability and free probability, we want to investigate whether similar non-central results hold in the free probability setting. This leads to the definition of the non-commutative fractional Brownian motion. In passing, we will also prove the free counterpart of Breuer-Major theorem 7.2.
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© 2012 Springer-Verlag Italia
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Nourdin, I. (2012). Non-Commutative Fractional Brownian Motion. In: Selected Aspects of Fractional Brownian Motion. B&SS — Bocconi & Springer Series. Springer, Milano. https://doi.org/10.1007/978-88-470-2823-4_8
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DOI: https://doi.org/10.1007/978-88-470-2823-4_8
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2822-7
Online ISBN: 978-88-470-2823-4
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