A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4 |
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| Authors: | Ivan Nourdin |
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| Institution: | Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Boîte courrier 188, 4 Place Jussieu, 75252 Paris Cedex 5, France |
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| 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. |
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| Keywords: | Fractional Brownian motion Weak convergence Change of variable formula |
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