In this paper, we study the order of convergence of the Euler-Maruyama (EM) method for neutral stochastic functional differential equations (NSFDEs). Under the global Lipschitz condition, we show that the pth moment convergence of the EM numerical solutions for NSFDEs has order p/2 - 1/l for any p >= 2 and any integer I > 1. Moreover, we show the rate of the meansquare convergence of EM method under the local Lipschitz condition is 1 - epsilon/2 for any epsilon is an element of (0,1), provided the local Lipschitz constants of the coefficients, valid on balls of radius j, are supposed not to grow faster than log j. This is significantly different from the case of stochastic differential equations where the order is 1/2.
|Pages (from-to)||1194 - 1200|
|Number of pages||7|
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|Publication status||Published - 2012|
Jiang, F., Shen, Y., & Wu, F. (2012). A note on order of convergence of numerical method for neutral stochastic functional differential equations. Communications in Nonlinear Science and Numerical Simulation, 17(3), 1194 - 1200. https://doi.org/10.1016/j.cnsns.2011.08.013