A remark on the covariance matrix of fractional Brownian motion

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  • remark on the covariance matrix of fractional Brownian motion

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Let X^H(t) be a fractional Brownian motion with index H (0<H≤1/2), and let D_n(t_0, t_1, ... t_n) (0≤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.

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