Faculté des sciences

Further remarks on mixed fractional Brownian motion

Thäle, Christoph

In: Applied Mathematical Sciences, 2009, vol. 38, p. 1885-1901

We study linear combinations of independent fractional Brownian motions and generalize several recent results from [10] and [17]. As a first new result we calculate explicitly the Hausdorff dimension of the sample paths of such processes. Moreover we compare different notions of fractional differentiability and calculate as a second new result explicitly the Cesáro fractional derivative of the... Plus

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    Summary
    We study linear combinations of independent fractional Brownian motions and generalize several recent results from [10] and [17]. As a first new result we calculate explicitly the Hausdorff dimension of the sample paths of such processes. Moreover we compare different notions of fractional differentiability and calculate as a second new result explicitly the Cesáro fractional derivative of the critical oder. Moreover we consider the more interesting absolute Cesáro fractional derivative and calculate its value explicitly.