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

Abstract

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.

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• On the rough-paths approach to non-commutative stochastic calculus
• Parameter estimation for rough differential equations
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• Numerical Schemes for Rough Parabolic Equations
• Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering