On the signature and cubature of the fractional Brownian motion for H>12

Riccardo Passeggeri

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1226-1257

Abstract: We present several results concerning the fractional Brownian motion (fBm) for H>1∕2. First, we show that 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, we show that, for the 2k-th term in the signature, the coefficient of the rate of convergence is uniformly bounded by Ãk(2k−1)(k−1)!2k. Third, we show that the 2k-th term of the expected signature is bounded by 1k!2k. Finally, we develop the general cubature method for the fBm for H>1∕2 for small times and provide a numerical example.

Keywords: Fractional Brownian motion; Signature; Rate of convergence; Sharp decay rate; Cubature method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:3:p:1226-1257

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DOI: 10.1016/j.spa.2019.04.013

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