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

Ivan Nourdin

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arXiv · 0806.2248

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

Ivan Nourdin

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Abstract

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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BibTeX RIS

Ivan Nourdin. 2008-10-03. A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4. https://arxiv.org/abs/0806.2248

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