On the non-commutative fractional Wishart process. (English) Zbl 1362.60040
The authors study the properties of the process of eigenvalues of a fractional Wishart process defined by \(N=B^*B\), where \(B\) is the matrix fractional Brownian motion investigated by D. Nualart and the last author [Stochastic Processes Appl. 124, No. 12, 4266–4282 (2014; Zbl 1301.60051)]. If the matrix process \(B\) has entries given by independent fractional Brownian motions with Hurst parameter \(H \in (1/2,1),\) the authors derive a stochastic differential equation for the eigenvalues of the corresponding fractional Wishart process and obtain a functional limit theorem for the empirical measure-valued process of eigenvalues of the fractional Wishart process.
Reviewer: B. L. S. Prakasa Rao (Hyderabad)
MSC:
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60F17 | Functional limit theorems; invariance principles |
| 60B20 | Random matrices (probabilistic aspects) |
Keywords:
fractional Wishart matrix process; eigenvalues; stochastic differential equation; functional limit theorem; measure-valued process; Young integral; fractional calculusCitations:
Zbl 1301.60051References:
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