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Convergence in law to operator fractional Brownian motion of Riemann-Liouville type. (English) Zbl 1263.60034

Summary: We extend the well-studied fractional Brownian motion of Riemann-Liouville type to the multivariate case, and the corresponding processes are called operator fractional Brownian motions of Riemann-Liouville type. We also provide two results on approximation to operator fractional Brownian motions of Riemann-Liouville type. The first approximation is based on a Poisson process, and the second one is based on a sequence of i.i.d. random variables.

MSC:

60G22 Fractional processes, including fractional Brownian motion
60F17 Functional limit theorems; invariance principles
60G15 Gaussian processes
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