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

By Ivan Nourdin and Université Paris Vi

Abstract

Abstract: We prove a change of variable formula for the 2D fractional Brownian motion of index H bigger or 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

Topics: Key words, Fractional Brownian motion, weak convergence, change of variable formula
Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.371.3897
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