Abstract
Let {S , t ≥ 0} be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 < H < 1. Its main properties are studied. They suggest that S H lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which S H is not a semi-martingale.
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