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

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• 作者：Juan Carlos Pardo ; José-Luis Pérez…
• 关键词：Matrix fractional Brownian motion ; Measure ; valued process ; Free probability ; Young integral ; Fractional calculus
• 刊名：Journal of Theoretical Probability
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：29
• 期：4
• 页码：1581-1598
• 全文大小：468 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Statistics
  
• 出版者：Springer Netherlands
• ISSN：1572-9230
• 卷排序：29

文摘

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.