Strong convergence of the partially truncated Euler–Maruyama method for a class of stochastic differential delay equations

This paper establishes the convergence of a class of highly nonlinear stochastic differential delay equations without the linear growth condition replacing by Khasminskii-type condition, so the convergence criteria here may cover a wider class of nonlinear systems. Our aim is to propose the partially truncated Euler–Maruyama method for stochastic differential delay equations dy(t)=f(y(t),y(t−τ))dt+g(y(t),y(t−τ))dw(t) and consider the strong-L^q convergence for 2≤q<p under the local Lipschitz condition plus Khasminskii-type condition, and p is a parameter in Khasminskii-type condition.