The authors consider stochastic functional differential equations (SFDEs) with jumps of the form
with given , where is -dimensional,, ,, is an -dimensional Brownian motion, and is a scalar Poisson process.
Under a global Lipschitz condition they show that the th-moment convergence of Euler-Maruyama numerical solutions to SFDEs with jumps has the order for any . This is different from the case of SFDEs without jumps, where the order is for any . They consider also the mean-square convergence under a local Lipschitz condition.