A note on convergence rate of a linearization method for the discretization of stochastic differential equations

This note discusses convergence rate of a linearization method for the discretization of stochastic differential equations with multiplicative noise. The method is to approximate the drift coefficient by the local linearization method and the diffusion coefficient by the Euler method. The mixed method guarantees the approximated process converges to the original one with the rate of convergence Δt, where Δt is the time interval of discretization.