In this talk I present various results concerning the fractional Brownian motion (fBm) for H>1/2. First, the rate of convergence of the expected signature of the linear piecewise approximation of the fBm to its exact value is given by 2H. Second, for the 2k-th term in the signature, the coefficient of the rate of convergence is uniformly bounded by ck(2k-1)/[(k-1)!2^k], where c is a explicit constant. Third, the 2k-th term of the expected signature is bounded by 1/(k!2^k). Finally, I present the cubature method for the fBm for H>1/2 for small times.
Riccardo Passeggeri is a Lecturer in Statistics at Imperial College London. After graduating from Imperial College London with a PhD in Math, he took up a research postdoc position at the University of Toronto and a was a FSMP fellow at the LPSM (Sorbonne University). While studying for his joint MRes (at Imperial and at University of Reading), he was mainly supervised by Horatio Boedihardjo, who introduced him to the theory of rough paths.
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