A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion

By A. Deya, Andreas Neuenkirch, Samy Tindel. 2010

86 citations recorded by the source corpus.

In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second order Taylor expansion, where the usual Levy area terms are replaced by products of increments of the driving fBm. The convergence of our scheme is shown by means of a combination of rough paths techniques and error bounds for the discretisation of the Levy area terms.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/ea99d0f49814d723f153844677242b099356dc7f

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Citations in the corpus

Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2014, result): “There are also a number of results on the rate of convergence of Euler-type numerical schemes in this case; see, for instance, the paper by Deya, Neuenkirch and Tindel [4] for a Milstein-type scheme without Lévy area in the case 13 < H < 1 2 , the paper by Friz and Riedel [5] for the N -step Euler s”
Convergence rates for the full Gaussian rough paths (2011, background): “• Wong–Zakai (and Milstein) rates for the fractional Brownian rough path (level 2 only, Hurst parameter H > 1/3) were first discussed in [4].”