Projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition

Abstract

In this paper, we investigate a projected Euler-Maruyama method for stochastic delay differential equations with variable delay under a global monotonicity condition. This condition admits some equations with highly nonlinear drift and diffusion coefficients. We appropriately generalize the idea of C-stability and B-consistency given by Beyn et al. (2016) to the case with delay. Moreover, the method is proved to be convergent with order one-half in a succinct way. Finally, some numerical examples are included to support our theoretical results.