Euler Scheme for Some SDEs with Fractional Noise and Markov Switching

We consider the numerical approximation by means of the Euler scheme of the unique solution to a class of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm) with Hurst parameter $H \in (1/2, 1)$ and a Markov switching (MS). We first study the $d$-dimensional additive case, followed by a one-dimensional equation with multiplicative noise. The strong convergence of the scheme in a finite time interval is studied and a convergence rate is obtained. Some simulations are provided to show the application of the theoretical results.