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

Abstract

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 d y ( t ) = f ( y ( t ) , y ( t − τ ) ) d t + g ( y ( t ) , y ( t − τ ) ) d w ( 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.