Class MilsteinSDE

  • All Implemented Interfaces:
    DiscreteSDE

    public class MilsteinSDE
    extends Object
    implements DiscreteSDE
    Milstein scheme is a first-order approximation to a continuous-time SDE. It adds a term to the Euler scheme by expanding both the drift and diffusion terms to O(dt). \[ dX_t = \mu * dt + \sigma * \sqrt{dt} * Z_t + \frac{1}{2} \frac{d\sigma}{dt} * \sigma * dt * (Z_t^2 - 1) \]
    See Also:
    Wikipedia: Milstein method
    • Constructor Detail

      • MilsteinSDE

        public MilsteinSDE​(SDE sde)
        Discretize a continuous-time SDE using the Milstein scheme.
        Parameters:
        sde - a continuous-time SDE
    • Method Detail

      • dXt

        public double dXt​(Ft ft)
        This is the SDE specification of a stochastic process.

        This is an implementation of the Milstein scheme. \[ dX_t = \mu * dt + \sigma * \sqrt{dt} * Z_t + \frac{1}{2} \frac{d\sigma}{dt} * \sigma * dt * (Z_t^2 - 1) \]

        Specified by:
        dXt in interface DiscreteSDE
        Parameters:
        ft - a filtration
        Returns:
        the increment of the process in dt
      • getNewFt

        public Ft getNewFt()
        Description copied from interface: DiscreteSDE
        Get an empty filtration of the process.
        Specified by:
        getNewFt in interface DiscreteSDE
        Returns:
        an empty filtration
      • db

        public double db​(Ft ft)
        \[ \frac{d\sigma}{dt} \]
        Parameters:
        ft - a filtration
        Returns:
        \(\frac{d\sigma}{dt}\)