Convergence of EM Scheme for Neutral Stochastic Differential Delay Equations

Abstract: In this paper, we are concerned with convergence rate of Euler-Maruyama (EM) scheme for stochastic differential delay equations (SDDEs) of neutral type, where the neutral term, the drift term and the diffusion term are allowed to be of polynomial growth. More precisely, for SDDEs of neutral type driven by Brownian motions, we reveal that the convergence rate of the corresponding EM scheme is one half; Whereas for SDDEs of neutral type driven by jump processes, we show that the best convergence rate of the associated EM scheme is close to one half.