A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4

Details A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4 A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4

2008-06-13

arxiv.org/abs/0806.2248v2

Mathematics

Probability

16 pages; to appear in Journal of Functional Analysis

Scientific paper

We prove a change of variable formula for the 2D fractional Brownian motion
of index H bigger of equal to 1/4. For H strictly bigger than 1/4, our formula
coincides with that obtained by using the rough paths theory. For H=1/4 (the
more interesting case), there is an additional term that is a classical Wiener
integral against an independent standard Brownian motion.

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