Strong convergence of the fractional WIS Euler integrator for Lipschitz drifts

We prove a terminal strong convergence bound for the GfBm\_EM Euler integrator of a scalar stochastic differential equation driven by multiplicative fractional Brownian noise in the Wick--Itô--Skorohod sense. For every Hurst parameter \(H\in(0,1)\) and every autonomous globally Lipschitz drift, the root mean-square error is bounded by \(C h^{\min\{H+1/2,1\}}\), using exact samples of the same noise path. The drift need not have higher derivatives. Initial values may be zero, and solutions may cross zero. Conditional Gaussian averaging controls the signed quadrature error at each time scale. Summing those scales gives the fractional rate without an exponent loss. At the Brownian endpoint, time reversal and short intervals chosen by the distance from zero yield order one with polynomial localization constants.