Numerical approximation of nonlinear neutral stochastic functional differential equations - Zhou, Shaobo; Fang, Zheng (Journal of applied mathematics & computing, 2013)
The paper investigates numerical approximations for solution of neutral stochastic functional differential equation (NSFDE) with coefficients of the polynomial growth. The main aim is to develop the convergence in probability of Euler-Maruyama approximate solution under highly nonlinear growth conditions. The paper removes the linear growth condition of the existing results replacing by highly nonlinear growth conditions, so the convergence criteria here may cover a wider class of nonlinear systems. Moreover, we also prove the existence-and-uniqueness of the global solutions for NSFDEs with coefficients of the polynomial growth. Finally, two examples is provided to illustrate the main theory.