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

摘要

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-Lq convergence for 2≤q