Advances in the truncated Euler-Maruyama method for stochastic differential delay equations

Fei, Weiyin and Hu, Liangjian and Mao, Xuerong and Xia, Dengfeng (2020) Advances in the truncated Euler-Maruyama method for stochastic differential delay equations. Communications on Pure and Applied Analysis, 19 (4). pp. 2081-2100. ISSN 1534-0392 (https://doi.org/10.3934/cpaa.2020092)

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Abstract

Guo et al. [GMY17] are the first to study the strong convergence of the explicit numerical method for the highly nonlinear stochastic differential delay equations(SDDEs) under the generalised Khasminskii-type condition. The method used there is the truncated Euler–Maruyama (EM) method. In this paper we will point out that a main condition imposed in [GMY17] is somehow restrictive in the sense that the condition could force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is then to establish the convergence rate without this restriction.

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