A remark on the covariance matrix of fractional Brownian motion

Let X^H(t) be a fractional Brownian motion with index H (0<H&le;1/2), and let D_n(t_0, t_1, ... t_n) (0&le;t_0<t_1<...<t_n) denote the correlation matrix of {X^H(t_<k+1>)-X^H(t_k): k=1, ..., n-1}. In this paper the asymptotic behaviour of (1/n) log det D_n as n tends to ∞ is studied