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

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

2010-04-07

arxiv.org/abs/1004.1071v2

Statist. Probab. Lett. 80 (2010), no. 19-20, 1543-1550

Mathematics

Probability

Scientific paper

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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