Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes (Q2356605)

This paper introduces two variants of the Milstein method that satisfy a global monotonicity condition and have mean square convergence order one under certain assumptions. These variants are a split-step backward method and a projected method. The analysis uses stochastic C-stability and B-consistency that together imply strong convergence. Numerical results illustrate the theory.