A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion

Juan Carlos Pardo (), José-Luis Pérez () and Victor Pérez-Abreu ()
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Juan Carlos Pardo: Centro de Investigación en Matemáticas
José-Luis Pérez: IIMAS-UNAM
Victor Pérez-Abreu: Centro de Investigación en Matemáticas

Journal of Theoretical Probability, 2016, vol. 29, issue 4, 1581-1598

Abstract: Abstract A functional limit theorem for the empirical measure-valued process of eigenvalues of a matrix fractional Brownian motion is obtained. It is shown that the limiting measure-valued process is the non-commutative fractional Brownian motion recently introduced by Nourdin and Taqqu (J Theor Probab 27:220–248, 2014). Young and Skorohod stochastic integral techniques and fractional calculus are the main tools used.

Keywords: Matrix fractional Brownian motion; Measure-valued process; Free probability; Young integral; Fractional calculus; Primary: 60B20; 46L54; 60G22; Secondary: 60H07 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-015-0627-7

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