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Some properties of the sub-fractional Brownian motion. (English) Zbl 1124.60038
Summary: We study several properties of the sub-fractional Brownian motion (sub-fBm) introduced by T. Bojdecki, L. G. Gorostiza and A. Talarczyk [Stat. Probab. Lett. 69, No. 4, 405–419 (2004; Zbl 1076.60027), J. Theor. Probab. 17, No. 3, 717–739 (2004; Zbl 1074.60047) and Stochastic Processes Appl. 116, No. 1, 1–18 (2006; Zbl 1082.60024)] related to those of the fBm. This process is a self-similar Gaussian process depending on a parameter H(0,2) with non stationary increments and is a generalization of the Brownian motion. The strong variation of the indefinite stochastic integral with respect to sub-fBm is also discussed.
MSC:
60G15Gaussian processes
60G18Self-similar processes