When does fractional Brownian motion not behave as a continuous function with bounded variation?

Ehsan Azmoodeh; Heikki Tikanmäki; Esko Valkeila

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arXiv · 1004.1071

When does fractional Brownian motion not behave as a continuous function with bounded variation?

Ehsan Azmoodeh·Heikki Tikanmäki·Esko Valkeila

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Abstract

If we compose a smooth function g with fractional Brownian motion B with Hurst index H > 1/2, then the resulting change of variables formula [or It/^o- formula] has the same form as if fractional Brownian motion would be a continuous function with bounded variation. In this note we prove a new integral representation formula for the running maximum of a continuous function with bounded variation. Moreover we show that the analogue to fractional Brownian motion fails.

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Ehsan Azmoodeh, Heikki Tikanmäki, Esko Valkeila. 2010-04-07. When does fractional Brownian motion not behave as a continuous function with bounded variation?. https://arxiv.org/abs/1004.1071

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