I am trying to numerically solve an SDE with both white and colored noise that models a non-linear circuit: $$ dX_t = f(X_t) dt + \sigma_w dW + \sigma_c dC $$ where $W$ is a standard Brownian motion and $C$ is a fractional Brownian motion with Hurst exponent zero (corresponding to $1/f$ flicker noise in electronic circuits). I've found several references for the theory of SDEs with fractional Brownian motion, but not being a mathematician they are way over my head.

Could someone explain what's the harm in using, say, a strong order 2 method from Kloeden and Platen's book and just ignoring the fact that $C$ is colored?