Higham, Desmond J.; Mao, Xuerong; Stuart, Andrew M. Strong convergence of Euler-type methods for nonlinear stochastic differential equations. (English) Zbl 1026.65003 SIAM J. Numer. Anal. 40, No. 3, 1041-1063 (2002). The authors prove the strong convergence of Euler-type methods for nonlinear stochastic differential equations under less restrictive conditions than global Lipschitz-based theory. These less restrictive conditions include the diffusion coefficient being globally Lipschitz and the drift coefficient being Lipschitz under a one-sided condition. Reviewer: Kevin Burrage (Brisbane) Cited in 4 ReviewsCited in 344 Documents MSC: 65C30 Numerical solutions to stochastic differential and integral equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H35 Computational methods for stochastic equations (aspects of stochastic analysis) Keywords:backward Euler method; Euler-Maruyama method; finite-time convergence; moment bounds; nonlinearity; one-sided Lipschitz condition; split-step PDFBibTeX XMLCite \textit{D. J. Higham} et al., SIAM J. Numer. Anal. 40, No. 3, 1041--1063 (2002; Zbl 1026.65003) Full Text: DOI