A note on order of convergence of numerical method for neutral stochastic functional differential equations

作者：Jiang, Feng; Shen, Yi^*; Wu, Fuke

来源：Communications in Nonlinear Science & Numerical Simulation, 2012, 17(3): 1194-1200.

DOI：10.1016/j.cnsns.2011.08.013

• Neutral stochastic functional differential equations
• Euler-Maruyama (EM)
• Local Lipschitz condition
• Order of convergence

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 mean-square 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.

• 出版日期2012-3
• 单位中南财经政法大学; 华中科技大学