Selected Topics in the Generalized Mixed Set-Indexed Fractional Brownian Motion

In this paper, we explore the generalized mixed fractional Brownian motion in the set-indexed framework and generalize several recent results from Miao et al. (Lecture Notes and Math, Springer, New York, 2008), Zili (J. Appl. Math. Stoch. Anal. 30:1–9, 2006) and Thale (Appl. Math. Sci. 3(28):1885–1901, 2009). We present the characterization of generalized mixed set-indexed fractional Brownian motion (gmsifBM) by flows, and we extend some selected aspects to the gmsifBM for the following issues: stationary increments, self-similarity, long-range dependence, Hölder continuity, differentiability, Hausdorff dimension, etc.