com.numericalmethod.suanshu.stats.stochasticprocess.univariate.sde
Class Milstein

java.lang.Object
  com.numericalmethod.suanshu.stats.stochasticprocess.univariate.sde.Milstein

All Implemented Interfaces:

DiscretizedSDE

public class Milstein
extends java.lang.Object
implements DiscretizedSDE

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).

 dXt = μ * dt + σ * sqrt(dt) * Zt + 0.5 * σ' * σ * dt * (Zt2 - 1);
 

See Also:

Wikipedia: Milstein method

Field Summary

SDE	sde the continuous-time SDE specification

Constructor Summary

Milstein(SDE sde)
Discretize a univariate SDE using the Milstein scheme.

Method Summary

double	db(Ft ft)
double	dXt(Ft ft) This is the SDE specification of the stochastic process.
Ft	getNewFt() Get an empty filtration for the process.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

sde

public final SDE sde

the continuous-time SDE specification

Constructor Detail

Milstein

public Milstein(SDE sde)

Discretize a univariate 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 the stochastic process.

This is an implementation of the Milstein scheme.

Specified by:

dXt in interface DiscretizedSDE

Parameters:

ft - filtration

Returns:

the increment of the process in dt

getNewFt

public Ft getNewFt()

Description copied from interface: DiscretizedSDE

Get an empty filtration for the process.

Specified by:

getNewFt in interface DiscretizedSDE

Returns:

an empty filtration

db

public double db(Ft ft)