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arXiv · 1206.4291

On the sub-mixed fractional Brownian motion

Charles El-Nouty·Mounir Zili
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Abstract

Let ${S_t^H, t \geq 0} $ be a linear combination of a Brownian motion and of an independent sub-fractional Brownian motion with Hurst index $0 < H < 1$. Its main properties are studied and it is shown that $S^H $ can be considered as an intermediate process between a sub-fractional Brownian motion and a mixed fractional Brownian motion. Finally, we determine the values of $H$ for which $S^H$ is not a semi-martingale.

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Charles El-Nouty, Mounir Zili. 2012-06-19. On the sub-mixed fractional Brownian motion. https://arxiv.org/abs/1206.4291

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