Projected Euler method for stochastic delay differential equation under a global monotonicity condition
For researchers working on numerical methods for stochastic delay differential equations, this extends convergence theory to a broader class of equations with highly nonlinear coefficients.
The paper proves convergence of the projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition, achieving order 1/2 convergence. Numerical examples confirm the theoretical results.
This paper investigates projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition. This condition admits some equations with highly nonlinear drift and diffusion coefficients. We appropriately generalized the idea of C-stability and B-consistency given by Beyn et al. [J. Sci. Comput. 67 (2016), no. 3, 955-987] to the case with delay. Moreover, the method is proved to be convergent with order $\frac{1}{2}$ in a succinct way. Finally, some numerical examples are included to illustrate the obtained theoretical results.