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.
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Pardo, J.C., Pérez, JL. & Pérez-Abreu, V. A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion. J Theor Probab 29, 1581–1598 (2016). https://doi.org/10.1007/s10959-015-0627-7
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DOI: https://doi.org/10.1007/s10959-015-0627-7
Keywords
- Matrix fractional Brownian motion
- Measure-valued process
- Free probability
- Young integral
- Fractional calculus