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1 Department of Mathematics Lawrence, Kansas 2 Probabilités et statistiques IECL - Institut Élie Cartan de Lorraine 3 BIGS - Biology, genetics and statistics IECN - Institut Élie Cartan de Nancy, INRIA Lorraine

Abstract : In this note, we provide a non trivial example of differential equation driven by a fractional Brownian motion with Hurst parameter 1-3 < H < 1-2, whose solution admits a smooth density with respect to Lebesgue-s measure. The result is obtained through the use of an explicit representation of the solution when the vector fields of the equation are nilpotent, plus a Norris type lemma in the rough paths context.

Keywords : fractional Brownian motion rough paths Malliavin calculus hypoellipticity





Author: Yaozhong Hu - Samy Tindel -

Source: https://hal.archives-ouvertes.fr/



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