Asymptotic Error Distribution of the Euler Scheme for Fractional Stochastic Delay Differential Equations with Additive Noise

In this paper we consider the Euler scheme for a class of stochastic delay differential equations driven by a linear fractional α-stable Lévy motion with index H∈(0,1). We establish the consistency of the scheme and study the limit distribution of the normalized error process. We show that in the rough case, i.e. when H<1/α, the rate of convergence of the simulation error is of order ΔH+1−1/αn and that the limit process is once again the solution of an (semi-linear) SDDE.