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The Milstein scheme for stochastic delay differential equations without using anticipative calculus. (English) Zbl 1247.65005
Unlike {\it Y. Hu, S.-E. Mohammed} and {\it F. Yan} [Ann. Probab. 32, No. 1A, 265--314 (2004; Zbl 1062.60065)], the authors do not use anticipative integrals to analyse the Milstein scheme for stochastic delay differential equations. Their simple method is based on Taylor expansions of the coefficient functions. Under some assumptions which are satisfied in the case of finitely many discrete delays, they prove the first order strong rate of convergence for the Milstein scheme.

65C30Stochastic differential and integral equations
60H35Computational methods for stochastic equations
60H10Stochastic ordinary differential equations
34K50Stochastic functional-differential equations
34K28Numerical approximation of solutions of functional-differential equations
65L20Stability and convergence of numerical methods for ODE
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