Convergence of EM Scheme for Neutral Stochastic Differential Delay Equations

Jianhai Bao, Yanting Ji, Chenggui Yuan

Published 2015-11-24Version 1

In this paper, we mainly investigate the convergence rate of the Euler-Maruyama(EM) scheme for two classes of neutral stochastic differential delay equations (NSDDEs), one is driven by Brownian motion, the other is driven by pure jump process. The coefficients in both classes of NSDDEs maybe highly non-linear with respect to the delay variables. Under the polynomial conditions, the convergence rate of EM scheme for NSDDEs driven by Brownian motion is $\frac{1}{2},$ while the the convergence rate of EM scheme for NSDDEs driven by pure jump process is determined by the ratio between overall time $T$ and the delay $\tau$.