The Milstein scheme, named after Grigori N. Milstein, is a numerical discrete approximation scheme for stochastic differential equations.
There is an explicit and an implicit version of the Milstein scheme.
The Milstein scheme is the simplest scheme that achieves a higher strong order of convergence than the Euler scheme, namely 1.0.
Let
be an Itô stochastic differential equation with suitable functions. In one dimension, the Milstein scheme is the following approximation scheme:
The number is chosen to be between 0 and 1.