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We approximate the solution of some linear systems of SDEs driven by afractional Brownian motion $B^H$ with Hurst parameter $H\in(\frac{1}{2},1)$ inthe Wick--It\^{o} sense, including a geometric fractional Brownian motion. Tothis end, we apply a Donsker-type approximation of the fractional Brownianmotion by disturbed binary random walks due to Sottinen. Moreover, we replacethe rather complicated Wick products by their discrete counterpart, acting onthe binary variables, in the corresponding systems of Wick differenceequations. As the solutions of the SDEs admit series representations in termsof Wick powers, a key to the proof of our Euler scheme is an approximation ofthe Hermite recursion formula for the Wick powers of $B^H$.

Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus