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
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.