The truncated Euler-Maruyama method for stochastic differential delay equations

Guo, Qian and Mao, Xuerong and Yue, Rongxian (2017) The truncated Euler-Maruyama method for stochastic differential delay equations. Numerical Algorithms. ISSN 1017-1398 (https://doi.org/10.1007/s11075-017-0391-0)

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Abstract

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 Lp) 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.

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