com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.sde
Class Euler

java.lang.Object
  com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.sde.Euler

All Implemented Interfaces:

DiscretizedSDE

public class Euler
extends java.lang.Object
implements DiscretizedSDE

The Euler scheme is the first order approximation of an SDE.

 dXt = μ * dt + σ * sqrt(dt) * Zt;
 

Field Summary

SDE	sde the continuous-time multivariate SDE

Constructor Summary

Euler(SDE sde)
Discretize a multivariate SDE using the Euler scheme.

Method Summary

Vector	dXt(Ft ft) This is the SDE specification of a stochastic process.
Ft	getNewFt() Get an empty filtration for the process.
int	nB() Get the number of independent driving Brownian motions.

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 multivariate SDE

Constructor Detail

Euler

public Euler(SDE sde)

Discretize a multivariate SDE using the Euler scheme.

Parameters:

sde - a continuous-time SDE

Method Detail

dXt

public Vector dXt(Ft ft)

This is the SDE specification of a stochastic process.

dXt = μ * dt + σ * sqrt(dt) * Zt;

Specified by:

dXt in interface DiscretizedSDE

Parameters:

ft - filtration

Returns:

the increment of the process in dt

nB

public int nB()

Description copied from interface: DiscretizedSDE

Get the number of independent driving Brownian motions.

Specified by:

nB in interface DiscretizedSDE

Returns:

number of independent driving Brownian motions

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