The Truncated Euler-Maruyama Method for Stochastic Differential Delay Equations
It provides a theoretical guarantee for strong convergence of numerical methods for a class of stochastic delay equations, which is important for practitioners needing reliable approximations.
This paper proves strong convergence (in L^p) of truncated Euler-Maruyama numerical solutions for stochastic differential delay equations under a generalized Khasminskii-type condition, extending previous results that only showed convergence in probability.
The numerical solutions of stochastic differential delay equations (SDDEs) under the generalized Khasminskii-type condition were discussed by Mao [15], and the theory there showed that the Euler-Maruyama (EM) numerical solutions converge to the true solutions in probability. However, there is so far no result on the strong convergence (namely in L^p) of the numerical solutions for the SDDEs under this generalized condition. In this paper, we will use the truncated EM method developed by Mao [16] to study the strong convergence of the numerical solutions for the SDDEs under the generalized Khasminskii-type condition.