Discrete-time approximations of stochastic delay equations: The Milstein scheme

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On the Moments of the Modulus of Continuity of Itô Processes (2009, methodology): “[19], the strong rate of convergence of a Milstein scheme for SDDEs with point delay is shown to be of first order (in contrast to the order 1 2 of the Euler scheme).”
The Milstein Scheme for Stochastic Delay Differential Equations Without Using Anticipative Calculus (2012, methodology): “The Itô formula is not used at all and our proofs are much simpler than in [4].”