Smoothness of densities for area-like processes of fractional Brownian motion (Q1939560)

Consider a process \(B_t=(B_t^1,\dotsc,B_t^n)\) consisting of \(n\) independent fractional Brownian motions with the same Hurst parameter \(1/4<H<1/2\), and let \(A_t\) be a process of type \(A_t=\frac12\int_0^t\alpha(B_s,dB_s)\), where \(\alpha\) is an alternating bilinear map. The process \(A_t\) is of Lévy area type, and rough paths theory is needed in order to give a sense to it. It is proved that \(Y_t=(B_t,A_t)\) has a \(C^\infty\)-density for any \(t>0\). To this end, the classical procedure of Malliavin's calculus involving the Malliavin covariance matrix is applied; one also needs properties of Gaussian spaces.